integrated quality and production logistic ......abstract selective and adaptive assembly systems...

Politecnico di MilanoDepartment of Mechanical Engineering

Doctoral Programme In Mechanical Engineering

INTEGRATED QUALITY AND PRODUCTION

LOGISTIC PERFORMANCE MODELING FOR

SELECTIVE AND ADAPTIVE ASSEMBLY

SYSTEMS

Doctoral Dissertation of:

Dariush Ebrahimi Azarbayejan

Supervisors:

Prof. Marcello COLLEDANI

Tutor:

Prof. Roberto VIGANO’

The Chair of the Doctoral Program:

Prof. Bianca Maria COLOSIMO

2014 - XXVI Cycle

Abstract

Selective and adaptive assembly systems are found in several manufactur-

ing contexts, above all automotive and mechanical components manufac-

turing, where the tolerances imposed on the assembled product key fea-

ture are much tighter than the tolerances imposed on the sub-assemblies

key features. In addition, due to the increasing pressure on high precision

manufacturing and the development of on-line measurement technologies,

selective and adaptive assembly systems have attracted increasing interest

in emerging sectors such as micro-production, biomedical and e-mobility

industries. In fact, selective and adaptive assembly system consists in mea-

suring the key quality characteristics of each sub-assembly and classifying

the sub-assemblies into buffers according to the measurement outcome.

In this thesis, a new analytical method is developed that allows predicting

the integrated quality and production logistics performance of the selec-

tive and adaptive assembly systems. The accuracy of the method is shown

by comparison of the results with that of simulation. The method is used

to derive insights on the behavior of these complex class of manufactur-

ing systems. For instance, the effect of total buffer space and the effect

of number of quality classes on the performance measures of the system

is explored and analyzed. The results show that improved performance is

achieved towards existing solutions, which deal only with quality aspects.

For example, we showed that by employing selective and adaptive assembly

systems, high precision assemblies can be produced from low precision sub-

assemblies with the required production rate, at the cost of increasing the

complexity of the system logistics, the work-in-progress and of decreasing

the total production rate of the system.

In addition, we have applied the process adaptation in the manufacturing

process in order to reduce the discard rate of sub-assemblies in selective and

adaptive assembly systems. The proposed method is modeled within the

analytical performance measurement framework of the selective assembly

systems. Moreover, new flow control policies are proposed and analyzed

in order to reduce the discard rate of the selective assembly system where

process adaptation in the manufacturing process is infeasible.

Finally, the industrial benefits are shown by means of applications to two

real manufacturing context. First, producing electrical drives in Bosch com-

pany and then remote laser welding application for body-in-white produc-

tion in Jaguar and Land Rover company. We shown that the effective

throughput is remarkably increased by applying the selective assembly sys-

tem, although the total throughput is decreased. Moreover, in the first case

we have shown that the benefits of introducing more quality classes into

the selective assembly system are more visible as the tolerance on the key

feature of the final assembly is tightened.

To my father,

Dr. Habib Ebrahimi Azarbayejan,

and my mother,

Maryam Banoo Saraydarchi Toussi

Acknowledgements

The contributions of many different people, in their different ways, have

made this thesis possible. I would like to extend my appreciation especially

to the following.

I would like to express my sincere gratitude to my supervisor Dr.Marcello

Colledani for the support of my Ph.D study and research, for his moti-

vation, patience, and for providing me his great knowledge and experience.

His good advice always helped me to keep working when I faced the most

difficult obstacles of my research.

I would like to thank to Prof. Tullio Tolio, Prof. Bianca Colosimo, Prof.

Barbara Previtali and Prof. Giovanni Moroni for their insightful comments,

and the wonderful lessons through my Ph.D courses.

I would like to thank to all my colleagues in the Mechanical Engineer-

ing Department, who made my PhD program enjoyable and convenient. I

would like to thank especially to Anteneh Yemane, Andrea Ratti, Chanaka

Senanayake, Wahyudin Permana and Danial Ramin for their great accom-

pany and providing me their useful insights to my research. Besides my

colleagues, I would like to thank to our coordinator Dr.Sivia Barattieri for

her patience and her wonderful attitude to help me during my PhD program.

I am most grateful to my parents, Habib Ebrahimi Azarbayejan and Maryam

banoo Saraydarchi Toussi for their love and their spiritual support through-

out my life. Also, I would like to thank my sister, Tannaz, for her motiva-

tional and inspirational comments as well as her educational advice.

Last but not the least I would like to thank my family and my dear friends:

Mehdi Motesharei, Reza Motesharei, Toktam Saraydarchi, Navid Rezaee

and Sadegh Riyahi for their support and being the encouragement through

my PhD program.

Contents

List of Figures vii

List of Tables xi

1 Introduction 1

1.1 Current Manufacturing Environment and Systematic Challenges in As-

sembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Assembly Quality Improvement Policies . . . . . . . . . . . . . . . . . . 2

1.2.1 Traditional Assembly to meet the required assemble quality: The

sub-assembly level strategy . . . . . . . . . . . . . . . . . . . . . 2

1.2.2 Selective Assembly to meet the required assemble quality: The

assembly process level strategy . . . . . . . . . . . . . . . . . . . 3

1.3 Selective Assembly Systems . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3.1 Selective Assembly Applications . . . . . . . . . . . . . . . . . . 5

1.4 Selective Assembly Systems Literature Review . . . . . . . . . . . . . . 7

1.5 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Theoretical Background: Performance Evaluation Methods In Man-

ufacturing Systems 11

2.1 Importance Of Manufacturing Systems Performance Evaluation . . . . . 11

2.1.1 Simulations Models . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.2 Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Review of analytical models: Exact Methods and Approximate Methods 13

2.2.1 Exact Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.2 Approximate Methods . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.3 Traditional Assembly Systems Performance Measurement . . . . 18

iii

CONTENTS

3 Selective Assembly System Conventions, System Description and An-

alytical Performance Evaluation Methodology 21

3.1 Mechanical Assemblies Conventions . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 Manufacturing System Conventions . . . . . . . . . . . . . . . . 23

3.2 Selective Assembly System Description . . . . . . . . . . . . . . . . . . . 24

3.2.1 Manufacturing machines and inspection stations . . . . . . . . . 25

3.2.2 The Assembly Machine . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.3 Modeling Assumptions and Notations . . . . . . . . . . . . . . . 30

3.2.4 Deadlock States . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 System Performance Measures . . . . . . . . . . . . . . . . . . . . . . . 34

3.4 Two-level Decomposition Approach . . . . . . . . . . . . . . . . . . . . . 35

3.4.1 Buffer Level Decomposition . . . . . . . . . . . . . . . . . . . . . 38

3.4.1.1 Upstream Pseudo-machine . . . . . . . . . . . . . . . . 38

3.4.1.2 Downstream Pseudo-machine . . . . . . . . . . . . . . . 39

3.4.1.3 Building Block Analysis . . . . . . . . . . . . . . . . . . 40

3.4.1.4 Inputs to the MLD . . . . . . . . . . . . . . . . . . . . 41

3.4.2 Machine Level Decomposition . . . . . . . . . . . . . . . . . . . . 41

3.4.2.1 Sub-assembly Manufacturing Machines: Mx and My . . 41

3.4.2.2 Assembly Machine . . . . . . . . . . . . . . . . . . . . . 49

3.4.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4.4 System Performance Measures . . . . . . . . . . . . . . . . . . . 61

3.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.5.1 Accuracy testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4 Selective Assembly System Analysis 69

4.1 Selective Assembly System Behavior . . . . . . . . . . . . . . . . . . . . 69

4.2 The Effect of More Quality Classes for Selective Assembly Systems . . . 73

5 Selective and Adaptive Assembly Systems 81

5.1 Selective and Adaptive Assembly Systems Definition . . . . . . . . . . . 81

5.1.1 Process Adaptability Approach To Reduce The Discard Rate:

Analytical Approach . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.1.1.1 Sub-assembly Manufacturing Machine My . . . . . . . . 85

iv

CONTENTS

5.1.1.2 The Effect of Process Adaptation On the System Per-

formance . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.1.2 The Optimal Process Shift Design in Selective and Adaptive As-

sembly Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.1.2.1 Modeling Assumptions . . . . . . . . . . . . . . . . . . 91

5.1.2.2 Matching Probability Evaluation Method . . . . . . . . 93

5.1.2.3 Shift Design Optimization . . . . . . . . . . . . . . . . 94

5.1.3 The Effect of Optimal Process Adaptation on the System Perfor-

mance Applying Simulation Model . . . . . . . . . . . . . . . . . 100

6 Deadlock State Correction Policies 109

6.1 Assembly Level Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.2 Sub-assembly Manufacturing Level Policies . . . . . . . . . . . . . . . . 112

6.3 Numerical results of the deadlock correction policies . . . . . . . . . . . 114

6.3.1 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

7 Selective Assembly Application in Electrical Engine Production: Bosch

Case 135

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

7.2 Bosch Electrical Engine manufacturing system description . . . . . . . . 136

7.2.1 Manufacturing Stages . . . . . . . . . . . . . . . . . . . . . . . . 138

7.2.2 Modeling Approach . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.2.3 Characterization of the quality parameters . . . . . . . . . . . . 142

7.3 New Configurations For Rotor Manufacturing Line . . . . . . . . . . . . 143

7.3.1 Selective assembly with two quality classes connected to two buffers.143

7.3.2 Selective assembly with four quality classes connected to four

buffers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

7.3.3 Selective assembly with six quality classes connected to six buffers.149

7.3.4 Selective assembly with eight quality classes connected to eight

buffers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

7.3.5 Comparison of the four analyzed configurations . . . . . . . . . . 150

7.4 The Effect of Final Assembly Key Characteristic Tolerance Tightening

on The Effective Throughput . . . . . . . . . . . . . . . . . . . . . . . . 157

7.4.1 Experiments Results . . . . . . . . . . . . . . . . . . . . . . . . . 158

v

CONTENTS

8 Selective Assembly Application in Automotive Industry: Door As-

sembly in Jaguar and Land Rover Company 163

8.1 JLR Door Manufacturing System Description . . . . . . . . . . . . . . . 164

8.2 The New Configuration of Assembly System: Application of Remote

Laser Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

8.3 The New Configuration of Hybrid System including Selective Assembly

System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

9 Conclusion 187

References 191

vi

List of Figures

1.1 System Description of Selective Assembly System. . . . . . . . . . . . . 4

1.2 Piston Cylinder Assembly, where the clearance is the assembly key char-

acteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Application of Selective Assembly Systems in remote laser welding. . . . 6

2.1 Decomposition Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Assembly System Decomposition Example. . . . . . . . . . . . . . . . . 19

3.1 Selective Assembly System Topology . . . . . . . . . . . . . . . . . . . 25

3.2 Machine X system topology. . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Assembly Machine System Topology. . . . . . . . . . . . . . . . . . . . . 28

3.4 Deadlock state 1 for the Selective Assembly with two quality classes. . . 32

3.5 Deadlock state 2 for the Selective Assembly with two quality classes. . . 32

3.6 Two level decomposition approach for selective assembly systems. . . . 36

3.7 Buffer Level Decomposition for lx(1). . . . . . . . . . . . . . . . . . . . . 42

3.8 Markov model representing Mx characteristics. . . . . . . . . . . . . . . 43

3.9 State transition diagram for upstream Pseudo machine L(x1). . . . . . . 44

3.10 Markov model representing Ma characteristics. . . . . . . . . . . . . . . 52

3.11 State transition diagram for downstream Pseudo machine l(x1). . . . . . 52

4.1 Total throughput behavior as the total buffer space increases. . . . . . 71

4.2 Effective throughput behavior as the total buffer space increases. . . . . 72

4.3 WIP behavior as the total buffer size increases. . . . . . . . . . . . . . . 73

4.4 Total TH behavior as the number of quality classes increases. . . . . . . 76

4.5 The effective throughput behavior as the number of quality classes in-

creases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

vii

LIST OF FIGURES

4.6 System Yield behavior as the number of quality classes increases. . . . . 79

5.1 Three shift policy for adaptive production systems. . . . . . . . . . . . . 83

5.2 Markov model characterizing the Machine Y, My, with process adjust-

ments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.3 Pseudo machine state transition diagram. . . . . . . . . . . . . . . . . . 88

5.4 Effect of Shifts on System performance. . . . . . . . . . . . . . . . . . . 90

5.5 Five symmetric shifts of process mean for Y. . . . . . . . . . . . . . . . 92

5.6 Block Diagram for Problme 2. . . . . . . . . . . . . . . . . . . . . . . . . 95

5.7 Matching probability as a function of the number of shifts - Case 1. . . 97

5.8 Matching probability as a function of the number of shifts - Case 2. . . 100

5.9 Schematic representation of selective and adaptive assembly systems for

the experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.10 Observed throughput under different shifts designs for case 1. . . . . . . 106

5.11 Observed WIP under different shifts designs for case 1. . . . . . . . . . . 106

5.12 Observed throughput under different shifts designs for case 2. . . . . . . 107

5.13 Observed WIP under different shifts designs for case 2. . . . . . . . . . . 107

6.1 Assembly Level Policies: Reactive Class Mix. . . . . . . . . . . . . . . . 110

6.2 Assembly level policies: Preventive Class Mix. . . . . . . . . . . . . . . . 111

6.3 Assembly Level Policy: Buffer Level Dependent. . . . . . . . . . . . . . 112

6.4 Manufacturing machine level policies: System Level Discard. . . . . . . 113

6.5 Manufacturing machine level policies : System Level Discard 1 Machine. 114

6.6 Experiment1: Effective throughput behavior for proposed deadlock cor-

rection policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121









viii

LIST OF FIGURES



6.12 Experiment1: The discard rate for proposed deadlock correction policies. 127

6.13 Experiment2: The discard rate for proposed deadlock correction policies .128






7.1 Integrated Mototr Generator (Bosch). . . . . . . . . . . . . . . . . . . . 137

7.2 Schema of Current Manufacturing System. . . . . . . . . . . . . . . . . . 138

7.3 Approximation of the original Bosch layout with a multistage process-

chain model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.4 Selective Assembly of stacks: schematic view. . . . . . . . . . . . . . . . 144

7.5 Proposed configuration: Selective assembly system with two classes. . . 145

7.6 Distribution of the magnetic flux intensity of the coupled stacks applying

the selective assembly with two quality classes and normal assembly

strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

7.7 Proposed configuration: Selective assembly system with four classes. . . 147


the selective assembly with four quality classes and normal assembly

strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

7.9 Distribution of the magnetic flux intensity of the coupled stacks apply-

ing the selective assembly with six quality classes and normal assembly

strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

7.10 Proposed configuration: Selective assembly system with six classes. . . . 150

7.11 Proposed configuration: Selective assembly system with eight classes. . . 151


the selective assembly with eight quality classes and normal assembly

strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

7.13 Reduction of variance with increasing number of quality classes. . . . . 153

7.14 Throughput total as the number of quality class increases. . . . . . . . . 155

ix

LIST OF FIGURES

7.15 Discard Rate as the number of quality class increases. . . . . . . . . . . 156

7.16 System Yield as the number of quality class increases. . . . . . . . . . . 157

7.17 Effective Throughput as the number of quality class increases. . . . . . . 158

7.18 Effect of tightening the tolerance on TH Eff. . . . . . . . . . . . . . . . 161

8.1 Current Assembly Sequence of Front door for model. . . . . . . . . . . 165

8.2 Precedence Diagram for the front door assembly line for the current

configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

8.3 Schematic layout of current manufacturing system for assembly line of

right and left front door (identical systems). . . . . . . . . . . . . . . . 167

8.4 Current manufacturing system model of the door assembly system. . . . 168

8.5 Graphical operation synthetic description . . . . . . . . . . . . . . . . . 169

8.6 Precedence Diagram for the front door assembly line for the new config-

uration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

8.7 The layout representing the new hybrid configuration. . . . . . . . . . . 178

8.8 Proposed configuration for left front and right front door including RLW

station with normal assembly system, focusing on the right front door. 182

8.9 Proposed configuration including the selective assembly system of two

classes for right side front door. . . . . . . . . . . . . . . . . . . . . . . . 183

8.10 Proposed configuration including the selective assembly system of three

classes for right side front door. . . . . . . . . . . . . . . . . . . . . . . 185

x

List of Tables

3.1 behavior of machine Mx. ”B” denotes blocking states, ”W” denotes

operational states, and ”R” denotes down states. . . . . . . . . . . . . . 46

3.2 Behavior of machine Ma. ”S” denotes starvation states, ”W” denotes

operational states, and ”R” denotes down states. . . . . . . . . . . . . . 50

3.3 Summary of the adopted parameters. . . . . . . . . . . . . . . . . . . . . 63

3.4 Range of variable parameters of accuracy test of analytical tool. . . . . . 63

3.5 experimental results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.1 Summary of the adopted parameters for more quality classes test. . . . 74

4.2 Partitioning limits for equal probability scheme. . . . . . . . . . . . . . . 75

4.3 Performance measures as the number number of quality classes increases. 77

5.1 Behavior of machine My. ”B” denotes blocking states, ”W” denotes

operational states, and ”R” denotes down states. . . . . . . . . . . . . 86

5.2 Summary of the adopted parameters. . . . . . . . . . . . . . . . . . . . . 90

5.3 Sample case data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.4 Maximum matching probability for a given number of shifts in Case 1. . 97

5.5 Binning and probabilities for Case 1, without process adaptation. . . . . 98

5.6 Details results in the application of three alternative methods for Case 1. 99

5.7 Maximum matching probability for a given number of shifts in Case 2. . 100

5.8 Binning and probabilities for Case 2, without process adaptation. . . . . 101

5.9 Details results in the application of three alternative methods for Case 2. 102

5.10 Case 1: Simulated total throughput and WIP for different shifts designs

(3* denotes the 3-shifts design proposed by Kannan and Jayabalan [2002]).105

xi

LIST OF TABLES

5.11 Case 2: Simulated total throughput and WIP for different shifts designs

(3* denotes the 3-shifts design proposed by Kannan and Jayabalan [2002]).108

6.1 Experimental plan for deadlock correction policies. . . . . . . . . . . . . 116

6.2 Performance measures results for experiment 1. . . . . . . . . . . . . . . 117






7.1 Mean time to failure, mean time to repair and cycle time of the machines. 142

7.2 Capacity of each buffer in the current manufacturing system[number of

stacks]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

7.3 Equal probability partitioning scheme for four quality classes. . . . . . . 147

7.4 Equal probability partitioning scheme for six quality classes. . . . . . . . 150

7.5 Equal probability partitioning scheme for eight quality classes. . . . . . 152

7.6 Performance measures of the proposed Selective Assembly configurations. 154

7.7 Tested Tolerance Limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.8 Performance Measures for the tolerance limit divided by 2 (T/2). . . . . 160



8.1 Current Manufacturing System Station Description. . . . . . . . . . . . 172

8.2 Summary of parameters of the current manufacturing system, adopted

for analytical performance measurement method. . . . . . . . . . . . . . 174

8.3 Summary of parameters of the proposed manufacturing system, adopted

for analytical performance measurement method . . . . . . . . . . . . . 177

8.4 Operation Synthetic of the new hybrid proposal including both RLW

and RSW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

8.5 Performance measures of the proposed manufacturing system with no-

selective assembly system. . . . . . . . . . . . . . . . . . . . . . . . . . . 181

8.6 Performance measures of the proposed manufacturing system for selec-

tive assembly system of 2 and 3 quality classes. . . . . . . . . . . . . . . 186

xii

1

Introduction

1.1 Current Manufacturing Environment and Systematic

Challenges in Assembly

In the current manufacturing environment, we observe an increasing complexity of the

products design and their applications. In addition, day by day products contains more

kinds of technologies, including electronics, mechanics and optics. For example, looking

at the new product such as cellphones and cameras or laptops, we can observe the fact

that they are becoming more performing and also they are being made in wide vari-

ety of versions, which means recognition of customers taste that is crucial to survive

for industries. Additionally, complexity of the new products and level of technology

that they required, push companies towards more precision in assembly process as well

as upstream manufacturing phases. However, variation is the physical results of any

manufacturing processes: components and assemblies are different from what we want

them to be although they are suppose to be identical. As a result, the actual value of

each component’s key characteristic will deviate from the desired value. In fact, in the

assembly process, manufactured sub-assemblies variation will accumulate via chains of

frames that pass through the sub-assemblies. The net result of these variations gener-

ates the final assembled product key characteristic variations. If the generated variation

on the key characteristic of the final product becomes more than its defined tolerance

limits the product is identified as non-conforming and it will be scraped.

This must be noticed that, customers request for a lower price and higher quality leads

1

1. INTRODUCTION

to the fact that only those companies who provide lower price and higher quality would

survive. However, complexity of new designed products acts conversely to lowering the

price and improving the quality. Therefore, it is crucial to propose an efficient approach

to improve the quality of the final assembled product, while reducing the production

cost to meet the customers requirements.

1.2 Assembly Quality Improvement Policies

Final assembly is the moment of truth, where all the upstream processes from design

and logistic to engineering and manufacturing with the aim of creating an object to

function specific task, are brought together. In the other words, an assembly process

is more than joining parts together. In fact, people and companies who are involved in

any stage of product development are forced to work together closely in order to obtain

the good assembled product. Otherwise the final product never become successful in

the final integration, i.e., the assembly process. Naturally, the upstream processes such

as manufacturing process are influenced strongly by assembly process through imposing

the tolerances on key characteristics features of any single sub-assembly. Although the

assembly is an important and influential process for the whole company, in this thesis

we focus on the link between the assembly process and its impact on the system level

domain, specifically in terms of final assembly quality and logistics performance of the

assembly systems.

1.2.1 Traditional Assembly to meet the required assemble quality:

The sub-assembly level strategy

Considering the high level of quality and complexity of the assembled product, deter-

mining the limits of variations for each sub-assemblies through tolerance synthesis seeks

to put the hard bounds for tolerance limits of each sub-assemblies. In the sub-assembly

level strategy, imposing these hard bounds on the components’ tolerance is considered

as an approach to meet the required quality of assembled products, although increasing

the whole manufacturing time and cost. However, this approach can be inefficient since

for many manufacturing technologies, the possibility of processing the components with

2

1.3. SELECTIVE ASSEMBLY SYSTEMS

lower tolerances is limited due to inherent process capability constraints. Therefore,

improving the quality of each sub assemblies could cause the expenditure cost due to

technology improvement of the sub-assembly’s manufacturing processes. If the com-

pany’s expenditure cost is non-affordable for the company, hard bounded tolerance

limits on the sub-assemblies wide variation cause increasing level of non-conforming

products. In both cases, companies are under the huge cost pressure to be able to

produce sub-assemblies that are interchangeably conforming for assembly.

1.2.2 Selective Assembly to meet the required assemble quality: The

assembly process level strategy

The concept of selective assembly represents a formal approach to obtain the high pre-

cision assembled products from relatively low precision sub-assemblies. Therefore, this

approach allows to overcome the technological limitation which is imposed by manu-

facturing systems trough coordination in the assembly process. As a matter of fact, the

advances in sensor technology have provided the possibility of rapidly inspecting several

product characteristics in a short time, with high accuracy and in-line. Selective as-

sembly consist in performing in-line inspection and in partitioning the sub-assemblies

into quality classes, depending on the specific outcome of the measurement process.

Therefore, only the matched sub-assemblies form the compliant buffers are assembled.

In the selective assembly the sub-assemblies are treated as an individuals rather than

statistical identical members of an assemble. Selective Assembly is a system level

approach which is proposed when process variability is too large which cause the pro-

duction of sub-assemblies with high variation in their key quality characteristic and it

is not economical to imposed the hard bounds decided by tolerance synthesis.

1.3 Selective Assembly Systems

As shown in Figure 1.1, selective assembly system involves sub-assemblies manufactur-

ing machines, sub-assemblies storage area, and assembly machine. The first stage is the

sub-assemblies manufacturing part of these systems. Machines Mx and My are man-

ufacturing machines and are behaving identically. Mx manufactures the sub-assembly

X and in-line inspection station (showed in red square) measures the key characteristic

3

1. INTRODUCTION

Figure 1.1: System Description of Selective Assembly System.

of the manufactured sub-assembly. The measured sub-assembly is placed in one of the

dedicated buffers according to its key characteristics, which is the second part of selec-

tive assembly systems. Number of buffers for each sub-assembly is equal. Therefore,

each sub-assembly class has its own complaint sub-assembly, to be joint to. For example

buffer B1y contains sub-assemblies to be assemble to sub-assemblies in buffer B1

x. The

assembly machine, selects the compliant sub-assemblies and assembles them. Finally,

the final inspection categorize the conforming and non-conforming final assemblies.

As depicted in Figure 1.1 assembly machine is matching only the compliant sub-

assemblies therefore it is expected to obtain better system yield (fraction of conforming

assembled products). However, classification of the sub-assemblies by manufacturing

machines and matching the complaint sub-assemblies by assembly machine cause strong

complexity in system logistics. As a matter of fact, the selective assembly system trans-

lates a product quality issue into a system logistics issue.

Selective assembly is an expensive strategy and is suggested to be applied when the

alternative strategy, namely making each part accurately enough for interchangeability,

is even more expensive. The main additional cost of selective assembly is the increased

level of logistics complexity which results in the reduced productivity of such a system.

Although the logistic complexity is highly increased in this class of system, but it has

4

1.3. SELECTIVE ASSEMBLY SYSTEMS

Figure 1.2: Piston Cylinder Assembly, where the clearance is the assembly key charac-

teristics.

been practiced in several industries. In the following section we will demonstrate some

of applications of selective assembly systems in industries.

1.3.1 Selective Assembly Applications

In the past, selective assembly is applied to traditional sectors, such as mechanical com-

ponents production as shown in Figure 1.2. For example, consider a piston and cylinder

assembly where the tolerance on the clearance between the two components is narrower

than the dimensional variability of the two sub-assemblies. If the assembly system se-

lects two components randomly from the upstream storage, the clearance could easily

be either too tight or too wide. In both cases, the assembled product is scrapped.

Under the selective assembly logistic, only compliant pre-classified sub-assemblies are

assembled, thus allowing a tighter control of the clearance. In fact, selective assembly

in this particular case suggests matching the smaller piston with smaller cylinder and

larger pistons with larger cylinders.

However, due to the increasing pressure on high precision manufacturing and to the

development of advanced and fast measurement technologies supporting on-line appli-

5

1. INTRODUCTION

Figure 1.3: Application of Selective Assembly Systems in remote laser welding.

cations, selective assembly systems have attracted increasing interest in the last five

years, especially in fast growing sectors such as micro-production Lchte et al. [2012],

in renewable energy equipment production (large parts assembly in windmills, electri-

cal engine assembly in the e-mobility sector), and in the automotive body assembly

Ceglarek and Huang [2007].

For example, selective assembly has been suggested as an effective approach to support

tight dimensional control of part-to-part gap during remote laser welding operations in

the automotive industry FP7-2011-NMP-ICT-FoF [2012]. In this application, a tight

gap control is essential to ensure the high quality of the produced stitch, in terms of

mechanical properties and corrosion resistance. Typically, the gap cannot be smaller

the 0.1mm while processing zinc coated sheet metals. The risk of a smaller gap is

the explosion or ejection of molten weld metal caused by the escape of trapped high

pressurized zinc vapor. Moreover, the gap cannot be larger than 0.3mm. The reason is

the risk of lack of fusion and insufficient penetration of the stitch in the components.

Selective assembly can classify compliant sheet metals after forming in order to have

a homogeneous gap between components during the welding process, contributing to

high quality welding. This requires the inspection-based characterization of the geo-

metrical variation of the metallic sheets. The measured data can be characterized by

statistical modal analysis Ceglarek and Huang [2007]. Figure 1.3 shows the application

of selective assembly systems in the remote laser welding technology.

6

1.4. SELECTIVE ASSEMBLY SYSTEMS LITERATURE REVIEW

Another recent application of selective assembly is found in the production of electrical

engines for the e-mobility sector FoF.NMP.2011-5 [2011]. Electrical engines are ob-

tained by assembling rotor and stator. The rotor is formed by a group of magnetic

stacks. Each stack has a set of magnets mounted on the external surface. The produc-

tion process involves the assembly of the magnets on each stack and the subsequent

magnetization of the entire stack. Then, the stacks are axially assembled to form the

rotor. However, due to the variability of the magnetization process, the magnetic field

intensity of the stacks are highly inhomogeneous, directly affecting the magnetic torque

of the final engine. Therefore, by classifying the stacks according to their field profile

and by selectively assembling the stacks in the rotor it is possible to reduce the variabil-

ity of the magnetic field intensity and to increase the stability of the engine magnetic

torque. We proposed the implementation of the selective assembly system in the cor-

responding manufacturing system of electrical engines production. The final chapter

of this thesis is dedicated to the analysis of the proposed system configuration, which

implies the positive effects of the selective assembly systems comparing to the current

configuration.

1.4 Selective Assembly Systems Literature Review

In the literature, the performance of selective assembly systems has been addressed by

mainly focusing on the effect of the partitioning design (also named sorting policy or

selection policy) on the assembled product quality. Partitioning is often based on two

schemes, i.e. equal width and equal probability partitions. In equal width scheme all

the assembled products can have the clearance within the tolerance limit, because the

sub-assemblies’ partitions have equal width in terms of key characteristic distribution.

However, in the cases that the key characteristic distributions of sub-assemblies are dis-

similar there will be a large number of sub-assemblies waiting for the their compliant

sub-assemblies in partitions (In the literature these sub-assemblies are called surplus

components). In equal probability scheme, sub-assemblies are partitioned into quality

classes with the equal probability for each sub-assembly. In this scheme, in case of

imbalanced key characteristic variation distributions there will be a fraction of rejected

assembled products although the surplus sub-assemblies could be reduced to zero. In

Mease et al. [2004] the authors propose optimal partitioning strategies under several

7

1. INTRODUCTION

loss functions and distribution assumptions, considering situations in which only one

of the components is partitioned as well as situations in which both components are

partitioned. They showed that zero-defect assembly is possible at the cost of drastically

increasing the number of quality classes, thus highly complicating the system logistics.

In [Kannan and Jayabalan, 2001a], an algorithm for minimizing the surplus compo-

nents in selective assembly is developed through defining the new partitioning design

for three sub-assembly assembly system. They showed that the number of partitions

are reduced, the surplus components are considerably minimized while the tolerance

of the final assembly is respected. Fang and Zhang [1995] proposed a partitioning

strategy based on equal probability scheme. They proposed a recursive algorithm to

define the partitioning of the sub-assemblies after the manufacturing within the certain

tolerances.Shun Matsuuraa [2007] provided optimal partitioning methodology under

squared loss errors, taking into consideration the measurement error influence. In Kan-

nan and Jayabalan [2001b],they proposed equal width partitioning scheme in case the

tolerance of clearance is smaller than the difference of three times the standard devi-

ation of the sub-assemblies key characteristics, otherwise equal probability scheme is

proposed. Kannan et al. [2005] provided a method to reduce the number of surplus sub-

assemblies as well as variations in clearance. These studies are typically supported by

statistical methods and do not consider the impact of the sorting policy on production

logistics related performance. Often the better quality of the final assembly is obtained

by increasing of the number of partitions. While at the same time ,more partitions

increase the system logistic complexity. Recently, simulation approach has been used

for predicting the impact of specific adaptation policies (Halubek et al. [2010], Kayasa

and Herrmann [2010]) on the system performance. They have applied the simulation

approach to support planning and control of the adaptable production systems.

These works typically neglect important production logistics features and the realistic

settings of the system, such as finite capacity buffers and unreliable machines. By doing

so, a relevant problem is neglected, i.e. the arising of deadlock states in the system that

need to be handled are avoided. Although selective assembly improves the quality of the

final assembly, but it complicates the logistic of such a systems which cause deteriorating

the productivity. As a matter of fact, an integrated quality and logistic performance

framework and an analytical methodology to support the design of selective assembly

8

1.5. THESIS CONTRIBUTIONS

systems have never been proposed, reducing the potential benefit of these systems in

industry. Considering the integrated quality and productivity framework to analyze

the selective assembly systems, we can answer the important questions like “What

is the impact of the number of partitions on the throughput of conforming assembled

products?” or “How limited buffers impact the system performance”. Otherwise, the

consequent configuration corresponds unbalanced and sub-performing system adopted

in industry.

1.5 Thesis Contributions

In this thesis we focus on developing an integrated framework of quality and produc-

tion logistic performance for selective assembly systems. A new approximate analytical

method for the prediction of the throughput of conforming products, the system yield

and the WIP in these systems is developed for the first time. Also, we proposed a new

deadlock correction policy based on the process adaptability of manufacturing systems.

The proposed method is developed in an analytical method. Several new intelligent

flow control policies based on the observable system state is proposed to improve the

performance of the selective assembly systems. We showed that the proposed policies

outperform the current policies for deadlock avoidance through the developed simula-

tion model.

Finally, we have proposed a new algorithm for optimal design of adaptable manufac-

turing systems that supply the sub-assemblies of selective assembly systems. In this

method we proposed the optimal approach for alternating the process target value to

minimize the surplus components of selective assembly system. The system level effect

of the optimal design of adaptable manufacturing system has been analyzed as well.

9

1. INTRODUCTION

10

2

Theoretical Background:

Performance Evaluation Methods

In Manufacturing Systems

2.1 Importance Of Manufacturing Systems Performance

Evaluation

In this chapter we will review the literature on the performance evaluation tools for

the system-level performance of manufacturing systems. In any manufacturing system

there are many random events that interrupt the production, such as machine failures.

These random events complicate the performance estimation of any manufacturing

systems and cause the unpredictable behavior of these systems. In addition, starvation

and blocking phenomenon caused by the machine failures can propagate through the

line. For example, a machine could remain starved (idle) because one of the upstream

machines is failed and there is no part in upstream buffer, or the machine could become

blocked because one of the downstream machines is failed and there is a downstream

buffer which is full. Often, it is suggested to increase buffers between machines to cover

the randomness of the events, which results in better throughput. However, the storage

space could be very expensive and limited most of the time. Moreover, increasing the

buffers often complicate the logistic systems and practitioners tend to avoid it.

11

2. THEORETICAL BACKGROUND: PERFORMANCEEVALUATION METHODS IN MANUFACTURING SYSTEMS

2.1.1 Simulations Models

Simulation models of manufacturing systems are widely used in system engineering

area. Simulation has the advantage of being flexible and is able to model a wide set of

systems, at the desired level of detail. Simulation most negative effect appears when

manufacturing systems need real-time decision makings, since simulation models require

high computational time to obtain statistically reliable results. When uncontrollable

manufacturing events (such as machine failures) happen some decision must be made

in real-time, such as process routing change or alternating the product scheduling for

flexible manufacturing systems. Alden et al. [2006] reported the inefficiency of simula-

tion models for on-line performance evaluation of the manufacturing systems due to the

long model creation time as well as complicated validation process. Simulation models

are generally suggested as an off-line tool to be used to evaluate the performance of

manufacturing systems and identify existing improvement possibilities. Application of

simulation models adopted for performance evaluation of manufacturing systems can

be found in [Bley et al., 1997, Phillis et al., 1997].

2.1.2 Analytical Models

Analytical models, tends to provide us with deeper understanding of the system and

they are usually much faster than the simulation models. The analytical model of

an assembly line can be imbedded in an optimization algorithm. The optimization

algorithm usually maximizes the throughput by running the analytical model several

times with different system characteristics and it takes few seconds to run these models.

In this way, analytical models can be applied to design manufacturing lines. Simulation

model could be imbedded to the optimization algorithm as well but it takes much more

time comparing to analytical models.

In this thesis we use both types of models. First, we developed a new an analytical

method to estimate the system performance of the selective assembly system. Then in

order to approve the precision of analytical method results, we compared several cases

to the developed simulation model.

12

2.2. REVIEW OF ANALYTICAL MODELS: EXACT METHODS ANDAPPROXIMATE METHODS

2.2 Review of analytical models: Exact Methods and Ap-

proximate Methods

In the literature there are several analytical methods which are introduced to help

manufacturing system engineers estimate the performance of complex systems. We

have differentiated all the analytical methods into two main methods that we review

here, exact analytical methods and approximate analytical methods.

2.2.1 Exact Methods

The exact models are better than the approximation method for cases that fit the real

system closely. In fact, in the approximate methods the exact models are the essential

part of solution due to the rapid solution.

In this section, we review the exact solutions of two-machine transfer lines with

unreliable machines and finite buffers. These systems are modeled as Markov processes

with discrete states and continuous times, as well as Markov processes with discrete

states and discrete times, and as Markov processes with mixed states and continuous

times.Buzacott, 1972 Buzacott [1972] describes a two-machine model with identical

unreliable machines and buffer in middle. Implicitly, he assumed that Both the opera-

tion times and repair times are geometrically distributed.Gershwin and Berman [1981]

investigated the two-machine system in which processing times, times to failure, and

times to repair are all exponentially distributed. They study the two-machine line when

two machines are different.Berman [1982] generalizes the Gershwin and Berman [1981]

considering the processing times to have Erlang distributions.

Buzacott [1967] and Buzacott [1969] proposed an exact method for two-machine sys-

tems when both the failure and the repair processes are geometric or deterministic. He

assumed that the probability that two events happen during the same cycle is negligi-

ble.Artamonov [1977] proposed a method to solve a two-machine line with deterministic

processing time and geometric repair and failure times, without considering the Buza-

cott [1967] and Buzacott [1969] assumption (probability that two events happen during

the same cycle is negligible). The method proposed in Gershwin [1994] (which itself

was a modification of Buzacott [1967]) is extended in Tolio et al. [2002] for unreliable

machines with multiple failure modes. They showed that approximating the failure

13


modes into a single failure mode which is proposed in Gershwin [1994] overestimated

the production rate of the two machine systems. Gershwin and Schiek [1983] extended

the analytic solution of the deterministic two-machine model of Gershwin [1994] to

three machines. To do this, they had to extend the analysis of internal states and the

analysis of boundary states, which is complicated. A boundary state is characterized

by a state where at least one of the buffers is on the boundary. The resulting tech-

nique was slow and practical only for small buffers. Considering the exact method of

performance analysis, the number of states of the Markov chains grows very fast with

the number of machines, the buffer capacities, and the number of phases of the dis-

tributions. Consequently, only models of limited sizes and with limiting assumptions

can be solved with the exact solutions. In the next section therefore we discuss the

main achievement of the approximate analytical methods to evaluate the performance

of longer manufacturing lines.

2.2.2 Approximate Methods

It comes into view that exact solutions of two-machine flow lines are available for a

both reliable machine and unreliable machines. However, it appears very difficult to

expect to obtain exact solutions of flow lines with more machines. Even the researches

on three-machine lines shows models that are too limited to be applicable, or they are

subject to numerical problems. Therefore, applying the approximate methods is the

only feasible alternative.

Several authors have developed approximation methods, which they call them ag-

gregation methods. The basic idea of aggregation is to substitute a two-machine-one-

buffer sub-system by a single equivalent machine. The equivalent machines has the

same throughput in isolation as the two-machine-one-buffer sub-system. Thus, an ag-

gregation method for analyzing a line with K machines consists in applying K-1 single

aggregation steps in forward and backwards. Performance measures such as through-

put rate of the system can be obtained when the algorithm converges.

Aggregation methods investigated mainly by Meerkov for Bernoulli, geometric and ex-

ponential machine reliability models, as mentioned in Li et al. [15 July 2009]. The main

advantage of the Meerkov aggregation method is that all the aggregation procedures

have been analytically proved to be convergent. In addition, he has studied several

14


system properties such as bottleneck analysis. Also, Li [2004] and Li and Meerkov

[2003] worked on aggregation methods to estimate the approximate performance of

manufacturing lines.

An alternative approximation method is decomposition which has been applied in a

wide variety of manufacturing system performance evaluation analysis. The idea is to

decompose the original manufacturing model into the set of smaller subsystems which

are easier to analyze. As mentioned in Dallery and Gershwin [1992], each decomposi-

tion method is developed through three steps: (1) characterizing the subsystems; (2)

developing a set of equations that derive the unknown parameters of each subsystem;

and (3) developing an algorithm to solve these equations. First, the original system

must be decomposed into subsystems and then each subsystem must be characterized.

The subsystems must have exact solutions. In the second step relationships between

quantities referring to different subsystems will be established so that the parameters

of each subsystem can be derived from the parameters and performance measures of

other subsystems. In general, the decomposition methods decompose a K-machine

manufacturing system (involving flow lines or any complex architecture) into a set of

K-1 subsystems, each subsystem being associated with the buffer of the original manu-

facturing system. Practically, decomposition methods are approximations because (1)

the decomposed subsystems are simpler than the whole system, and so cannot cap-

ture the same behavior properly; and (2) some of the developed equations applied to

determine the parameters can be approximate. In decomposition methods, there is

an important trade-off between complexity and accuracy. Of course, a more complex

characterization of the subsystems will lead to a better approximation of the behavior

of the original system and, therefore, to more accurate results. However, obtaining the

more accurate solution of subsystems will also be more complex and, since each sub-

system is usually solved in iterative algorithms, the overall computational complexity

become greater.

Decomposition methods have been developed either for flow lines with reliable ma-

chines or for flow lines with unreliable machines. In this thesis we have considered

the two-machine one buffer line for each decomposed subsystem and which is named

building block. Each building block is associated with a buffer of the original line. Let

L denote the original line and let L(i, i+ 1) denote the building block associated with

15


Figure 2.1: Decomposition Method.

buffer B(i, i + 1). Furthermore, we use superscripts u and d to refer to objects and

parameters of the upstream and downstream machines. Machine Mu(i, i + 1) is the

upstream machine of the building block L(i, i + 1), and Md(i, i + 1) represents the

downstream machine, as graphically depicted in the 2.1.

Note that machine Md(i − 1, i) in line L(i − 1, i) and machine Mu, (i, i + 1) in line

L(i, i + 1) correspond to machine Mi of the original system. It is assumed that the

capacity of the buffer of each building block is the same as that of the corresponding

buffer of the original system.

The basic idea of decomposition is to characterize the upstream and downstream ma-

chines for each building block L(i, i + 1) in such a way that the material through its

buffer behaves close to the behavior of material in buffer B(i,i+1) in the original system.

That is, an observer in the buffer of line L(i, i+1) would see virtually the same arrivals

and departures, starvation and blocking, and buffer level dynamics as an observer in the

buffer of the original system. Exact solutions of the building blocks can be obtained, as

described earlier. The details of the decomposition method can be found in Gershwin

[1987], Choonga and Gershwin [1987], DALLERY et al. [1988] and DALLERY et al.

16


[1989].

Wide variety of analytical performance evaluation method have been developed by ap-

plying the the decomposition methods. Analytical performance evaluation methods of

More complicated manufacturing systems have been proposed by extending and improv-

ing the decomposition method. A set of new decomposition equations are developed in

Gershwin and Burman [2000] to evaluate the assembly/disassemble systems. The pro-

posed equations cover the complex propagation of blocking and starvation probabilities

along the line. In Colledani et al. [2005] and Colledani et al. [2208] multiple produc-

tion manufacturing systems have been analyzed. In order to apply the decomposition

method a two-machine line dedicated to each product type have been generated. In

Colledani et al. [2005] Markovian analysis of the behavior of the flexible machine pro-

ducing two part types is performed. The same class of manufacturing systems of multi-

ple part type has been studied in Jang and Gershwin [2007] while they have proposed an

exact method for a new type of two machine systems. An analytical performance evalu-

ation method to analyze the continuous flow manufacturing systems when machines are

characterized by general Markovian fluid models is proposed in Colledani and T.Tolio

[2011]. They have proposed a set of new decomposition equations to capture the prop-

agation effects of partial and complete blocking and starvation phenomena throughout

the system. In Colledani and T.Tolio [2005] proposed an approximate analytical ap-

proach based on decomposition method for modeling and evaluating the performance

of manufacturing systems involving split and merge of material flow, multiple product

systems, assembly/disassembly manufacturing systems when buffer capacity is finite.

Some other methods have applied the decomposition method for developing perfor-

mance evaluation method of manufacturing systems including quality aspects. Tem-

pelmeier and Burger [2001] proposed a decomposition method for the performance

evaluation of multi-stage production lines in which the no-conforming parts are scraped

by the system. Helber [2000] proposed a new decomposition method for performance

evaluation of manufacturing systems with split of material flow for rework and scrape.

In Gershwin and J.Kim [2005] they have analyzed the performance of manufacturing

systems monitored by Jikoda practice of stopping the manufacturing line as soon as

non-conformists are identified. The authors proposed a method to characterize the

17


manufacturing machines with a discrete state-continues time Markov chain to observe

the machine states while machine is operating the good parts, machine is operating

bad parts and finally states in which machine is not working. They have applied the

decomposition technique to develop the performance evaluation model of the studied

system. In Colledani and T.Tolio [2006] authors applied the decomposition method to

develop performance evaluation model for manufacturing systems monitored by SPC

with online inspection. They have considered both 100 percent inspection and sampling

policies in their model. In Borgh et al. [2007] they have extended the Colledani and

T.Tolio [2006] approach to the analysis of manufacturing systems with online quality

control systems and rework of non-conforming components. In Colledani and T.Tolio

[2009] an approximate analytical method is developed based on system decomposition

for evaluating the manufacturing systems monitored by SPC, including scrape and fi-

nite buffers explicitly.

The decomposition method attracted interests of practitioners in several manufacturing

context as well. For instance, in Patchong et al. [2003] they have developed an analytical

approach based on decomposition method combined with simulation model to analyze

and improve the performance of car body shop of SPA Peugeot Citroen. Alden et al.

[2006] reported an application of analytical approach based on decomposition method

for performance evaluation in several sectors of General Motors. Colledani et al. [2010]

proposed a new methodology, based on analytical methods, to support SCANIA in

manufacturing system productivity improvement through re-configuration. The ana-

lytical approach is based on the decomposition and the application of this approach to

the SCANIA six-cylinder engine-block machining line enabled a remarkable increment

in throughput by selecting analytically the most suitable improvement actions.

2.2.3 Traditional Assembly Systems Performance Measurement

To get insights about the sub-assembly level strategy of the final assemble quality im-

provement, we need to study the performance of traditional assembly systems from the

system point of view. There are wide verity of research conducted in this area.

The first comprehensive survey which is conducted in analysis of performance of assem-

bly system is Gershwin [1991]. He described a single part type assembly-disassembly

18


Figure 2.2: Assembly System Decomposition Example.

production system as a network with discrete material, unreliable machines, and fi-

nite buffers. In order to evaluate the overall performance of the system in terms of

production rate and average buffer levels, he proposed to decompose the system to

two-machine, one buffer lines which is called building block. The flow of material in

the buffer of each building block approximates the behavior of the original system.

He has developed equations that relates the original line machines’ parameters to the

building block machines’ parameters. In order to solve the decomposition equations,

he applied the Otero-DDX algorithm which is based on Dallery-David-Xie (DDX) al-

gorithm (DALLERY et al. [1988]). Otero-DDX is an algorithm which propose the

evaluation sequence of the building blocks of assembly/dis-assembly models. Figure

2.2 represents an example of the decomposition application in the assembly system

performance evaluation method.

19


Mascolo et al. [23(4] focused on the system similar to the Gershwin [1991], while they

have consider the continuous flow of the materials in assembly line. Therefore the

features of the system that they have considered are: homogenous assembly lines, un-

reliable machines with exponential failure and repair times, and finite buffer capacities.

The systems of single part type, homogenous assembly-disassembly production system

with continuous material, exponential failure and repair time distributions unreliable

machines, and finite buffers is considered in Gershwin and M.Burman [2000]. By inho-

mogeneous he means the machines processing times could be different along the line.

The author developed decomposition equations in order to approximate the machines

behavior in decomposed building blocks. He has proposed an algorithm to solve de-

composition equations which follows the DDX algorithm and its extension, the ADDX

algorithm (M.Burman [1995]), however the proposed algorithm reduced the computa-

tional time.

JEONG and KIM [1998] proposes an efficient method to estimate the throughput and

average buffer levels of Assembly/Disassembly systems. They have studied an Assem-

bly/Disassembly system which has the finite buffer capacities, repair time and failure

time are distributed exponentially, and the processing time of machines are different

and they are distributed exponentially as well. They use the decomposition approach

to estimate the performance of the line. Equations to compute the failure, repair and

processing times of each building block is derived based on the interruption of flow, re-

sumption of flow and the flow rate-idle time relations. Different but fixed processioning

time has been studied in Gershwin and M.Burman [2000], but JEONG and KIM [1998]

proposed an algorithm to transfer stochastic processing time to homogenous system in

such a way that the transferred system performs close to the original system.

20

3

Selective Assembly System

Conventions, System Description

and Analytical Performance

Evaluation Methodology

In this thesis we have two sets of conventions for our modeling procedure of selective

assembly systems, the first set is regarding to the assembly process and we call them

Mechanical Assemblies Conventions and the second set of conventions is regarding to

the manufacturing system level assumptions and we call this set System level Conven-

tions.

3.1 Mechanical Assemblies Conventions

1- Key Characteristic Distributions Of The Sub-assemblies.

we assumed that there are models for how the key characteristic of sub-assemblies are

distributed statistically. The partitioning techniques for selective assembly and the

scrapes that we have to impose to sub-assemblies are based on these distributions. In

practice, these data are collected from the history of the manufacturing process there-

fore the actual data are used to generate the statistical distributions, while in cases

that are not available, the nominal process mean value is considered as the distribution

mean and the standard deviation is estimated from the similar characteristics in a simi-

21

3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY

lar production environment (Whitney [2004]). In addition, the key characteristic values

of sub-assemblies are an independent random variables because the manufacturing er-

ror, which is the variation cause, is composed by several independent error sources.

According to Central Limit Theorem (Miller and Miller [2004]) the key characteristic

(for example the dimension) can follow normal distribution when there is no significant

source of error.

2- No Process Mean Drift.

Commonly, in manufacturing processes due to tool wear out or using a different mate-

rial and so on, there are process mean drift which cause the shift in the mean nominal

value. We assume that in manufacturing process Statistical Process Control is applied

and there are no mean drift.

3- Assembly Task Time and Assembly Error.

We assume sub-assemblies can be placed simply in correct location and orientation

during assembly process. This can be done reliably and repeatably, and does not need

operator skills. Therefore, assembly process is well suited for mass production and

assembly task time is homogeneously with the other manufacturing processes.

4- Single Key Characteristic For The Sub-assemblies.

We assume that through mathematical engineering analysis of sub-assemblies’ key char-

acteristic on the assemble key characteristic (AKC), there is only a single sub-assembly

key characteristic (only dimensional and not geometric) that final assembly quality is

sensitive to. In practice it is suggested to minimize the number of influential key char-

acteristic of sub-assemblies on the quality of final assembly.

5- Rigid Body Sub-assemblies (no deformations).

There are no variation buildup in assembly due to the sub-assemblies stress-strain con-

siderations (Whitney [2004]). For example, in sheet metal parts fabrication, process

contains forming and die machines which cause variations due to spring-back phe-

nomenon. Therefore, to simplify our model we assume that part have no spring-backs

and no stress-strain effects on the assembled part variations.

22

3.1. MECHANICAL ASSEMBLIES CONVENTIONS

6- Measurement Error.

There is no significant measurement error, and by significant we mean sub-assemblies

will not be mixed in terms of quality classes in dedicated buffers due to measurement

error. In addition, considering no measurement error, there are no confirming parts

who are rejected and there are no non-conforming parts accepted both in manufactur-

ing stage and assembly stage.

3.1.1 Manufacturing System Conventions

1- Two Sub-assemblies.

In this thesis we study the assembly system which assembles two components to ob-

tain the final product. In real world, products are consist of several sub-assemblies

and rarely we can find an assemble consist of two components, however assuming two

separate sets of components and considering each set as a single sub-assembly is not

far from reality. Therefore, we assign one key characteristic for each set of components

and we consider it as unique sub-assembly key characteristic.

2- Stations Integration.

Sub-assemblies are made through several operations and naturally there is no single

stage manufacturing process. We assumed all the manufacturing elements are aggre-

gated in a single station for each sub-assembly production (we have two manufacturing

stations according to Manufacturing System Conventions 1) and the same applies for

assembly station. Beside, both the manufacturing machines are fully dedicated to the

assigned sub-assemblies. Therefore, machines capacity are all equal to 1 for each sub-

assembly manufacturing as well as assembly process.

3- Human Resource Interaction.

We assumed human resource are available and reliable all the time and there is no dis-

ruptions due to labor resource. Therefore, if production rate increases, although labor

relations may suffer, but we ignore the effect to simplify the system analysis.

4- No System Learning.

When essential system disruption happens in manufacturing system, managers usually

23


try to find the source of disruption and they prevent that disruption to happen again.

However, we assume that we respond to disruption by introducing buffers to the system

so that the disruption can be mitigated. Therefore, when any machine fails its adja-

cent machine may continue the operation. Therefore, in this thesis we ignore system

learning because we prefer to study the performance of the fixed system first, then

uncertainty of parameters (for example uncertainty of failure and repair parameters)

could be studied in future complementary studies.

3.2 Selective Assembly System Description

A typical system of the proposed class is represented in Figure 3.1. Although this sys-

tem can be extended into a wider process-chain, including upstream component man-

ufacturing processes and downstream manufacturing processes for further processing

of the assembled component, in this thesis we will specifically focus on the integrated

quality and production logistics performance of the selective assembly cell. Specifically,

we consider a selective assembly system where two sub-assemblies, namely X and Y,

are assembled. Extensions to higher number of sub-assemblies are possible, within the

same framework.

As shown in Figure 3.1 the sub-assemblies X and Y are respectively processed by ma-

chines Mx and My (blue squares). After the manufacturing process, each sub-assembly

is inspected (red squares) and placed into the dedicated buffers (yellow circle), accord-

ing to the measured key quality characteristic value.

For sub-assembly X (or Y ) the dedicated buffers are denoted as Bix(or Bi

y ) with

i=1,...,F. Buffers have finite capacity N ix and N i

y , with i=1,...,F. A sub-assembly X

is assembled with one sub-assembly Y of the same class by the assembly station Ma

(light blue rectangle).

The detailed characteristics of the manufacturing machines and inspection stations

and the characteristics of the assembly machine are discussed in the following, with

particular emphasis on the policies regulating their part flow control mechanisms.

24

3.2. SELECTIVE ASSEMBLY SYSTEM DESCRIPTION

Figure 3.1: Selective Assembly System Topology

3.2.1 Manufacturing machines and inspection stations

In the described system, both Mx and My are manufacturing machines dedicated to

the sub-assembly X and Y manufacturing process, respectively. However, since they

share the same system behavior, we will focus on the description of Mx. Without loss

of generality, the same notation is applied for the sub-assemblies manufactured in My

with proper modification of sub/superscription.

As illustrated in Figure 3.2, Mx is an integrated machine formed by two stages in se-

ries. The first stage is the machining station which processes the key feature of the

component; the second stage is an inspection station dedicated to the on-line measure-

ment of the processed quality feature. After inspection and based on the sub-assembly

quality feature measurement, the processed sub-assembly is deposited in one of the

downstream buffers. For regulating this process, a partitioning policy is defined so that

the measured sub-assemblies are characterized by their quality class. Each quality class

is connected to the specific buffer, therefore, manufactured sub-assemblies are deposited

in dedicated buffers based on key quality characteristics.

The machine Mx is unreliable and it fails while producing a sub-assembly x with prob-

ability Px = 1/MTTFx and it is repaired with probability rx = 1/MTTRx. Time

to failures are assumed to be geometrically distributed. From a material flow point

25


Figure 3.2: Machine X system topology.

of view, the sub-assembly manufacturing and inspection station Mx acts as a splitting

stage, that sorts the incoming material flow into F output flows. However, the splitting

fractions are not fixed and known a priory but they depend on the sub-assembly key

characteristic distribution.

Component quality. Stage Mx produces parts with key quality characteristic values

distributed according to a known probability density function fx (As mentioned in

conventions, the statistical distribution of the sub-assemblies key characteristic is known

and fix). The mean of the distribution is µx and the standard deviation is σx. On this

feature, Specification Limits are imposed by design process. They are defined as Upper

Specification Limit (USLx) and Lower Specification Limit (LSLx). According to these

limits, a component can be defective if its quality characteristic is out of the defined

limits. Defective components x are identified and scrapped by the inspection station

located downstream of manufacturing machine Mx. The manufacturing processes of

sub-assemblies X and Y may have different capabilities.

Partitioning Policy. When a sub-assembly is manufactured, its key quality feature

is measured and it is partitioned into a specific quality class according to the mea-

sured value. For sub-assembly X, Cx quality classes are defined. Each class contains

sub-assemblies with key quality feature values included between two limiting values.

Therefore, for each quality class cx, the lower limit lXcx and the upper limit LXcxof the

quality feature belonging to that class are defined. The quality classes are contiguous,

i.e they respect the following properties:

26


LXcx = lXcx+1 ∀cX = 1, ..., Cx − 1 (3.1)

LCx = USLX

l1 = LSLX

In the case of equal width partitioning scheme for partitioning,

LXcx − lXcx =

USLX − LSLXCX

∀cX = 1, ..., CX (3.2)

In general definitions, the number of quality classes generated for sub-assemblies x

and y is the same, i.e. CX = CY . Equation 3.3 defines the sorting policy, αXcx is the

probability of sorting a part after inspection into quality class cx:

αXcx =

∫ LXcx

lXcx

Fx(s)ds (3.3)

Each quality class cx is connected to the specific buffer BXi , with i = 1, ..., F . It means

there is a one-to-one association between buffers and quality classes.

3.2.2 The Assembly Machine

The assembly station Ma assembles one sub-assembly X with one sub-assembly Y to

meet a desired key quality characteristic value of the assembled product, shown in

Figure 3.3. From a material flow point of view, the assembly station Ma acts as a

merging stage, that merges the F incoming material flows into a unique output flow

while each flow has an assembly operation. Stage MA is unreliable and it fails while

producing a part with probability Pa = 1/MTTFa and it is repaired with probability

ra = 1/MTTRa. Times to failures and time to repairs are assumed to be geometrically

distributed.

Assembled product quality. We denote z as the key quality characteristics of the

assembled product which is expressed in form of a function z = g(x, y) of the sub-

assemblies’ key quality feature values x and y. Therefore, the probability density func-

tion fz and the cumulative distribution function Fz can be obtained by the cumulative

27


Figure 3.3: Assembly Machine System Topology.

distribution functions of x and y. Specification Limits are imposed by design on the

assembly key characteristic z. They are defined as Upper Specification Limit (USLz)

and Lower Specification Limit (LSLz). If the value of z exceeds these limits, the as-

sembled product is non-conforming. According to this tolerance, every assembly flow

has a specific fraction of non-conforming parts associated, namely γai , with i = 1, .., F .

For example, consider the aforementioned application of the remote laser welding pro-

cess in the automotive industry. In this case, the gap between the key quality feature of

sub-assemblies X and Y is the key quality feature z of the assembled product. In more

details, the key quality characteristic of the final assembly is the weld stitch quality

that strictly depends on the gap between the two metallic plates to be welded. The

gap (z) is measured and controlled and have to be | x− y | to generate the proper weld

stitch. In case of z = g(x, y) ≤ 0.1 the gap is too tight and the vaporized zinc has no

space to flow out of the welded metals and cause porosity in the welds stitches. On the

other hand, if z = g(x, y) = |x− y| ≥ 0.3 the gap is too high and the two metals cannot

be joint properly due to lack of fusion. In both cases the final assembly is identified as

non-conforming part (Steen [1993]).

If a unique quality class is present for components X and Y , i.e. selective assembly

is not adopted, the fraction of defective assembled products can be directly estimated

28


from the cumulative function Fz and the specification limits imposed on z. However, in

selective assembly the assembled products are generated by matching specific quality

classes, cx and cy, of the sub-assemblies. Therefore, for each possible combination of

quality classes of X and Y , cx and cy, the normalized cumulative function FZcx,cy has

to be computed, for example by convolution. Then, the fraction of generated defective

products γ (cx, cy) for each matched class be calculated as:

γ(cx, cy) = 1− F zcx,cy(USLz) + F zcx,cy(LSLz) (3.4)

Matching Policy. A matching policy couples a buffer of sub-assemblies X with one

compliant buffer of sub-assemblies Y . In this thesis, a one to one matching between

buffers of component X and Y is assumed. In other words, the assembly machine Ma

can assemble components X in buffer Bxi only with sub-assemblies Y in buffer By

i , with

i = 1, ..., F . Therefore, F possible output flows are generated, obtained by joining the

sub-assemblies in the F existing buffers.

Assembly Policy. The assembly machine selects the compliant buffers according to

a probabilistic rule, similar to the part type selection rule proposed in (Colledani et al.

[2005]). If all the upstream buffers are not empty, which is all the coupled buffers are

available to be selected, than the assembly machine selects buffer i with fixed proba-

bility αai , with∑F

i=1 αai = 1. If one or more upstream buffer is empty, the selection

probability is scaled according to the available components. If all the upstream buffers

are empty, the machine is starved.

It must be noticed that although both the assembly policy and the partitioning policy

(after the manufacturing processes) are probabilistic, there is a fundamental difference

between these policies. In the assembly policy there is always full control of the pro-

cess, in the sense that the assembly machine has the intelligence to decide which flow

is better to process. On the contrary, in the partitioning policy the quality class of a

given sub-assembly cannot be imposed a priory, but it is a result of measuring the key

quality characteristic which is a consequence of the process variation.

The smart property of the assembly machine for selection of the the proper flow, per-

mitted us to introduce new flow control policies to improve the material flow of selective

29


assembly systems. These policies show great improvement in the system performance

of selective assembly systems. We explained the policies in details and their effect in

the next chapter.

3.2.3 Modeling Assumptions and Notations

A list of modeling assumption that we have used in this thesis is described in the

following.

• The dynamics of the material flow is modeled as a discrete flow of parts. All

operational machines start their operations at he same instant. Therefore the

time is considered as discrete. Moreover, the states of the system are discrete.

• Each machine has the fixed and same processing time which is known in advanced.

The processing time is scaled to the time unit (synchronous manufacturing sys-

tem).

• Operational dependent failures: machine could fail only while processing a part.

Therefore, when the machine is blocked or starved (which is idle in general),

cannot fail.

• Each machine is unreliable and subject to multiple failure modes. Machine failures

are uncorrelated, i.e., they are independent of the state of the rest of the system.

• If operational, a machine starts processing one part at the beginning of the time

unit. The buffer levels are updated at the end of the time unit.

• The manufacturing machines are never starved, i.e., there is an infinite number

of sub-assemblies waiting to be manufactured upstream the Mx and My.

• The assembly machine is never blocked, i.e., there is enough space for sub-

assemblies to be deposited in downstream of MA.

• Blocking before service (BBS ): If the downstream buffer is full, the machine is

prevented from doing any operation.

• An operational machine can fail in only one of its failure modes.

30


• When a machine breaks down, the part it was processing on is returned to the

upstream buffer to wait for the machine to get repaired and process can resume.

• Inspection and transportation are assumed to take negligible time comparing to

the operations time.

3.2.4 Deadlock States

Observing the dynamic of system behavior, a deadlock state is observed due to the

system logistic complexity and finite buffer capacity. If all the following conditions

hold in the system, the associated state is called deadlock state:

1. Machine Mx cannot deposit sub-assembly X of quality class i in buffer Bxi since

it is full;

2. Machine My cannot deposit sub-assembly Y of quality class j in buffer Byj since

it is full;

3. The assembly machine MA cannot assemble parts from any couple of upstream

buffers because there are no complaint sub-assemblies to be assembled.

Figure 3.4 and Figure 3.5 describe better the deadlock states for the selective assembly

system with two quality classes. In the case of two quality classes, there are two separate

deadlock state that the system might visit. The black circles illustrate the full buffer

while the white circle shows the empty buffer. Observing Figure 3.4, the manufacturing

machine Mx and My are blocked because one of the downstream adjacent buffers are

full. They cannot start process because the processed sub-assembly might belong to

the full buffer class after measurement and following the Blocking Before Service (BBS)

rule the machine must be blocked. The assembly machine is starved because one of the

matched buffers contain no sub-assemblies for process, one sub-assembly buffer is full

while the other is empty. Figure 3.5 illustrates the same behavior of the system while

the full buffers are the opposite of the Figure 3.4.

31


Figure 3.4: Deadlock state 1 for the Selective Assembly with two quality classes.

Figure 3.5: Deadlock state 2 for the Selective Assembly with two quality classes.

32


To characterize more formally the deadlock state, considering the buffer levels described

by the vector n = (nx1 , nx2 , ..., n

xF , n

y1, n

y2, ..., n

yF ), a deadlock state is every state under-

going the following condition:

(nxi = Nxi ∧ n

yi = 0) or (nxi = 0 ∧ nyi = Ny

i ) ∀i = 1, ..., F (3.5)

Notice that we are required to design a selective assembly system which avoids visiting

the deadlock state. In deadlock state, the assembly machine is starved since there are

no upstream non-empty coupled buffers as the same time the manufacturing machines

(Mx and My) are blocked because one of their downstream buffers is full. Consequently,

the system is completely absorbed in deadlock state.

Deadlock avoidance policies. To avoid the deadlock state the following policies

have been introduced for these systems. According to (Thesen and Jantayavichit [1999])

two strategies are possible:

• Discard: discard incoming sub-assemblies that cannot be accommodated in the

selected full buffer.

• Ignore: allocate sufficient space to accommodate all space demand.

The discard policy is characterized by a strict partitioning policy is always followed,

i.e. each quality class is always dedicated to a unique buffer. Thus, whenever a sub-

assembly is produced, either at machine Mx or MY , that cannot be deposited in the

downstream buffer where this sub-assembly is sorted since this buffer is full, the sub-

assembly is discard and a new sub-assembly has to be processed by the machine. It

can be proved that under this policy the deadlock condition is never reached.

Although this policy entails a loss of throughput, it preserves the assembly yield (frac-

tion of conforming assembled parts). This is because the assembly machine remains

with the selection of sub-assemblies based on the pre-defined quality classes.

33


The total throughput, which is total production rate including the non-conforming

parts, is reduced due to the fact that the manufacturing stages are processing sub-

assemblies and when the station is blocked by a single buffer, they discard the pro-

cessed sub-assembly belonging to the corresponding full buffer. By doing this, there

are fraction of conforming sub-assemblies totally neglected for assembly process.

In real life manufacturing, discarding the sub-assemblies is mostly placing the compo-

nents out of the classification system, while sub-assemblies has its quality attribute and

there is possibility to be assembled.

The Ignore policy introduce a very high level of work in progress to the system in order

to avid the deadlock state which implicitly ignores the limited buffer sizes. Therefore,

in order to develop our analytical performance evaluation method, we considered the

discard policy to proceed.

3.3 System Performance Measures

To analyze the performance and system behavior of selective assembly systems the

main system performance measures of interest are:

• Average total production rate of the system, THTot:

the final assembled production rate [parts/time unit] delivered in output by the

system, considering both conforming and non-conforming assemblies. Starting

from the total production rate of every assembled flow i = 1, ..., F , it can be

derived as:

THTot =F∑i=1

THToti (3.6)

• Average effective production rate, THEff :

the final assembled production rate [parts/time unit] delivered in output by the

34

3.4. TWO-LEVEL DECOMPOSITION APPROACH

system, considering only conforming assemblies. It can be obtained as:

THEff =

F∑i=1

THToti Yi (3.7)

• System yield, Y system:

the fraction of conforming assemblies delivered in output by the system. It can

be obtained as the rate between the effective and the total throughput:

Y system =EEff

ETot(3.8)

• Average level of buffers, n̄xi and n̄yi :

the average amount of parts accumulated in each buffer.

• Average total Work in Progress, WIP:

the average number of parts flowing in the system.

WIP =n∑i=1

n̄xi +n∑i=1

n̄yi (3.9)

3.4 Two-level Decomposition Approach

In order to evaluate the performance of a selective assembly systems, an extension of

the decomposition technique proposed in Colledani et al. [2005] is used. The general

idea of the approach is the following: for each buffer in the original line, a building

block is dedicated that is formed by two pseudo-machines and one buffer, as represented

in the right side of Figure 3.6. Each building block is analyzed by using the method

in Tolio et al. [2002], and the results are propagated among sub-systems by using the

35


Figure 3.6: Two level decomposition approach for selective assembly systems.

so-called DDX algorithm proposed in DALLERY et al. [1988].

Since in the described selective assembly system the sub-assembly manufacturing ma-

chines act as split machines and the assembly machine acts as a merge station, their

behavior cannot be matched by simple multiple failure mode models. Indeed, more

than one input or output flows are available and this generates additional complexity

in the machine behavior. Therefore, they cannot be directly considered in the decom-

position. In other words, there is a gap between the structures of the Markov chains

modeling the behavior of the machines in our system and the structures of the Markov

chains accepted by available decomposition methods. Thus, a preliminary analysis of

these complex machines is needed. In fact, the proposed method to develop analytical

performance evaluation method differs from the classical decomposition. In Colledani

et al. [2005] a similar approach was applied to flexible machine processing multiple

part-types and the method was named Two-level Decomposition (Figure3.6).

The first level of analysis is based on the evaluation of all the state probabilities of each

station (two manufacturing machines, Mx and My and the assembly machine). These

36


probabilities are obtained by solving discrete time-discrete state Markov chains repre-

senting the behavior of such complex machines, also taking into account the influence

of their adjacent buffers. Considering the selective assembly system topology, there are

three Markov chains which represent the states of whole the system. In each Markov

chain, some of transition probabilities are not known. For example for Markov chain

representing the Mx there are probabilities of blocking which is unknown, similarly, for

Markov chain of Ma there are starvation probabilities which are unknown. However,

the starvation and blocking probabilities can be derived by studying the probabilities

of upstream buffers being empty and probabilities of downstream buffers being full,

respectively. This level of analysis is named Machine Level Decomposition (MLD) be-

cause the focus of analysis is on the machines states. This preliminary analysis allows

to approximately simplify the behavior of such complex machines with that of multiple

failure modes machines. With these machine models, it is possible to perform the clas-

sical multiple failure mode two-machine line analysis,(Tolio et al. [2002]) which is based

on the exact analytical solution of building block formed by two pseudo-machines and

one buffer.

This second level of analysis is focused on the flow of material crossing the buffer.

Indeed, we assign failure and repair parameters to the pseudo-machines of each build-

ing block in order to mimic the flow of material through the corresponding buffer of

the original line. Therefore, we name this level of analysis Buffer Level Decomposition

(BLD). The unknown parameters for each Markov chains, which is discussed above,

can be obtained from the results of each building blocks.

The order in which the MLD and the BLD are applied to the machines and buffers

in the line is controlled by an algorithm, similar to the DDX DALLERY et al. [1988].

By studying alternately the BLD and the MLD and by using the results obtained in

one level as input for the other level, it is possible to evaluate the performance of the

original complex system, once convergence conditions are met.

The Two-Level Decomposition approach is useful in those cases in which machines with

a complex behavior are included in the system. In this section, we present the analysis

performed in both levels and propose the equations for exchanging the parameters from

37


the MLD to the BLD and vice versa. The proposed method is explained in details for

the case of a selective assembly system with two sub-assemblies and two quality classes

F=2, i.e two buffers for each sub-assembly. The analysis and the proposed approach

are similar for the other system topologies in which more than two quality classes are

present for each sub-assembly.

3.4.1 Buffer Level Decomposition

The building block lx(i) is composed of two pseudo-machines Mu,x(i) and Md,x(i)

and the buffer Bx(i). The flow of material through the buffer Bx(i) of the building

block must approximate the flow of material through the corresponding buffer Bxi of the

original system. In order to achieve this goal, failure modes must be assigned to Mu,x(i)

and Md,x(i), relating them to each possible cause for interruption of the material flow

respectively entering and leaving the buffer.

3.4.1.1 Upstream Pseudo-machine

Considering the flow of material entering the original buffer Bx(i), it can be interrupted

for different reasons. For each possible cause of interruption of the material flow entering

the buffer Bx(i), a failure mode is assigned to the upstream pseudo-machine Mu,x(i).

In general for machines with split property there are two kinds of failure modes which

are assigned to the machine. The Modified Local Failure and the Competition Failure,

which are described in details in the following.

Modified local failure. The machine Mx in the original line may fail while pro-

cessing a sub-assembly. If the machine of the original system Mx fails, all the pseudo-

machines representing that machine in the building blocks must fail. For this reason,

local failure modes are assigned to Mu,x(i). It must be noticed that, for splitting ma-

chines, the probability of failure in local mode is not the same as the one of the original

machine Mx. It must be increased, considering the probability that the original ma-

chine fails while processing a sub-assembly which will be placed in the other buffer.

Therefore, the probabilities of local failures must be adjusted to take into account this

situation. The failure probabilities pu,xt (i) are therefore unknown and will be provided

in output by the MLD. The repair probabilities ru,xt (i) are instead the same as the

38


repair probabilities of the original machine Mx, i.e. ru,xt (i) = rxt , for each i = 1, 2 and

t = 1, .., Tx.

Competition failure. When a machine of the original system is operational (in

the UP state) but it is processing the sub-assemblies that will not be placed in the

buffer Bx(i) belonging to considered building block, the corresponding pseudo-machine

Mu,x(i) sees an interruption of flow (while the machine is actually operational) and is

considered to be failed. In the other words, although the machine is operational and

working, the processed sub-assembly will not be accommodated in the observed buffer.

This failure mode of the pseudo-machines was introduced for studying multiple part

type systems (Colledani et al. [2005]). The failure and repair probabilities pu,xTx+1(i) and

ru,xTx+1(i) are unknown and will be provided in output by the MLD.

3.4.1.2 Downstream Pseudo-machine

Considering the flow of material leaving the original buffer Bx(i), it can be interrupted

for different reasons. For each possible cause of interruption of the material flow leaving

the buffer Bx(i), a failure mode is assigned to the pseudo-machine Md,x(i). There

are three kind of material interruption flow which are considered as failure modes for

downstream pseudo machine, Modified Local Failure and Competition Failure which

are similar to upstream pseudo machine and the third mode is Remote Failure. In the

following each of these are described in details.

Modified local failure. The assembly machine MA in the original line may fail while

assembling the two sub-assemblies. If the machine of the original system MA fails,

all the pseudo-machines representing that machine must fail. For this reason, local

failure modes are assigned to Md,x(i). It must be noticed that, for a merging machine

performing assembly, the probability of failure in local mode is not the same as the

one of the original machine MA. It must be increased, considering the probability that

the original machine fails while assembling sub-assemblies taken from another couple

of matching buffers. The failure probabilities pd,xt (i) are therefore unknown and will be

provided in output by the MLD. The repair probabilities rd,xt (i) are instead the same

as the repair probabilities of the corresponding original machine MA, i.e. rd,xt (i) = ra

for each i = 1, 2 and t = 1, .., Tx.

39


Competition failure. When the assembly machine MA is operational but it is as-

sembling matching sub-assembly taken from a flow different from the considered buffer

Bx(i), the corresponding pseudo-machine Md,x(i) is considered failed (while the as-

sembly machine is operational). As mentioned earlier this failure mode of the pseudo-

machines is named Competition Failure. The failure and repair probabilities pd,xTx+1(i)

and rd,xTx+1(i) are unknown and will be provided in output by the MLD.

Remote failure. When the buffer Bx(i) is not empty but the machine Ma can-

not assemble parts from the considered flow i because the matching sub-assemblies

Y stored in the buffer By(i) are not available (i.e. By(i) is empty) the correspond-

ing pseudo-machine Md,x(i) is considered as failed machine. This failure mode of the

pseudo-machines is named Remote Failure, since the cause for the interruption of flow

comes from a different machine in the system. The failure probabilities pd,xTa+1+j(i) with

j = 1, .., Ty, are unknown and will be provided in output by the BLD. The repair

probabilities rd,xTa+1+j(i), with j = 1, .., Ty, are instead the same as the repair proba-

bilities of the pseudo-machine Mu,x(i), which is responsible for causing the starvation,

rd,xTa+1+j(i) = ru,yj (i), for each i = 1, 2 and j = 1, .., Ty.

3.4.1.3 Building Block Analysis

The analysis of the Building Block lx(i) can be performed by using the exact method

proposed in Tolio et al. [2002]. In particular, the average throughput THx(i) and the

average buffer levels, nx(i). Moreover, The blocking probabilities of Mu,x(i) are Pbxk(i),

k = 1, .., Ta + 1 + Ty which is a vector composed by blocking probabilities due to local

failures of assembly machine, competition failure of assembly machine and the local fail-

ure of the machine producing the sub-assembly Y. Similarly, the probabilities of Md,x(i)

being starved, Psxj (i), j = 1, .., Tx + 1, which is a vector of starvation probabilities due

to local failures of the machine processing sub-assembly X are calculated.

40


3.4.1.4 Inputs to the MLD

The BLD provides input information to the MLD analysis. In particular, the transitions

to blocking states for the MLD analysis of Mx are calculated as follows:

px,b,ik =Pbxk(i)

Ex(i)rx,b,ik i = 1, 2; k = 1, ..., Ta + 1 + Ty (3.10)

rx,b,ik (i) = rd,xk (i) i = 1, 2; k = 1, ..., Ta + 1 + Ty

Similarly, the transitions to starvation states for the MLD analysis of Ma are derived:

px,s,ij =Psxj (i)

Ex(i)rx,s,jj i = 1, 2; j = 1, ..., Tx + 1 (3.11)

rx,s,jj (i) = ru,xj (i) i = 1, 2; j = 1, ..., Tx + 1

The summary of the buffer level decomposition for building block lx(1) and the param-

eters which will be transferred to the machine level decomposition (MLD) is depicted

in Figure 3.7.

3.4.2 Machine Level Decomposition

In the buffer level decomposition analysis that we have explained above, there are input

and output parameters that we transfer to MLD. In this section we describe in details

the MLD analysis and the data transfer for each machine separately.

3.4.2.1 Sub-assembly Manufacturing Machines: Mx and My

State Transition Diagram. The Markov chain representing the behavior of the

sub-assembly manufacturing machine Mx is represented in Figure 3.8 (to simplify the

picture, transition probability p̄ is shown instead of 1 − p; moreover P1 =∑Tx

t=1 pxt +∑Ta+1+Ty

k=1 px,b,1k ).

The Markov chain of original machine is characterized by all the possible states that

the machine may observe. For example for each local failure mode a unique state is

41


Figure 3.7: Buffer Level Decomposition for lx(1).

42


Figure 3.8: Markov model representing Mx characteristics.

associated. However, in order to simplify the picture, in Figure 3.8 the Markov chain

of Mx is illustrating the macro states of the original machine. This means, all the

state of the same type are grouped into a unique aggregated state, without considering

the different failure mode. Each aggregated state is defined by two state indicators,

the first term refers to the first downstream buffer (Bx1 ) and the second refers to the

second downstream buffer (Bx2 ). Each state indicator can assume three different states,

Blocked (B), Working (W), and Down (R).

The aggregated states probabilities in steady state are obtained by adding up all the

43


Figure 3.9: State transition diagram for upstream Pseudo machine L(x1).

probabilities of the states of the same type. For example the probability of the aggre-

gated state (RB2) which indicates the state in which the machine is locally down while

the Bx2 is full, is obtained by adding up all the probabilities of the (RiB

2) states over

the local failure modes of the machine (π(· · · ) is indicating the steady-state probability

of the state in brackets)., i.e.,

π(RB2) =

Tx∑i=1

π(RiB2) (3.12)

It must be notice that while we have shown the aggregated states in the Markov chain

(Figure 3.8), in the writing the equations we have distinguished all the states based on

the failure modes to correctly valuate the Markov chain state probabilities. Obviously,

the machine Mx cannot be in both working and down state at the same time, thus the

states (R1W 2) and (W 1R2) are not feasible and not represented in the state transi-

tion diagram. Also the aggregated state (R1R2) represent the state in which both the

downstream buffers are not full and the machine is locally failed. This state is shown

as (R).

In the following we describe some characteristics of the Markov model representing the

Mx behavior,

• If the machine is working and both downstream buffers are not full, the state is

shown as (W 1W 2). Since machine is subject to local failures, from state (W 1W 2)

it may go into state (R) which is the down state. If one of the buffers become full

44


and the machine is still operating, machine state is shown as (W 1B2) or (B1W 2)

depending on the the full buffer.

• When the machine is in state (W 1B2) and the machine is operating, it may process

a sub-assembly which belongs to the second quality class after measurement. Due

to the fact that the second quality class is connected to the full buffer, the sub-

assembly is discarded based on the Discard rule for deadlock avoidance policy.

The probability of the discard in this state is π(W 1B2)αx2 . The same might

occur for the the state (B1W 2) when the machine processes a sub-assembly that

will be belong to the first quality class, the discard probability is obtained by

π(B1W 2)αx1 .

• When the machine is in the state (W 1B2) or (B1W 2), it mail locally fail and the

corresponding Markov chain goes to state (RB2) or (B1R).

• If the machine is in operating state and the two downstream buffers are both full,

the state is indicated as (B1B2). If the assembly machine selects the sub-assembly

from Bx1 , the Markov chain representing machine Mx goes to state (W 1B2) and

if the assembly machine selects the sub-assembly form Bx2 the Markov chain goes

to state (B1W 2).

Therefore, depending on the level of the adjacent buffers, machine Mx behaves, as re-

ported in summary in Table 3.1. As it can be noticed, the discard policy affects the

behavior of the machine in the states where one of the two buffer is full and the other

is not full (row 1 to row 4). The probability of failure and repair of machine Mx, i.e. px

and rx, are known since they are input data of the problem. It must be noticed that,

in the Markov chain of original machine Mx (similarly My), the competition failure is

not considered because this machine is able to produce for both quality classes, which

means for both buffers. In the other words, the Markov chain characterizes the original

machine and two adjacent downstream buffers, thus observes the states concerning two

possible quality classes.

As it can be noticed from the Markov chain, the probabilities of transition to blocking

states are unknown and cannot be derived directly from the original system. However,

through the appropriate equations in BLD (see equation 3.10: the unknown parameters

45


Buffers Part qualityMachine State

Discard Rule

Bx1 Bx

2 Class Output Buffer Prob.

Not Full Full 1 UP(W 1B2) Bx1 αx1

Not Full Full 2 UP(W 1B2) discard αx2

Full Not Full 1 UP(B1W 2) discard αx1

Full Not Full 2 UP(B1W 2) Bx2 αx2

Not Full Not Full 1 UP(W 1W 2) Bx1 αx1

Not Full Not Full 2 UP(W 1W 2) Bx2 αx2

Full Full 1-2 BL(B1B2) / /

Not Full Full 1-2 DOWN(RB2) / /

Full Not Full 1-2 DOWN(B1R) / /

Not Full Not Full 1-2 DOWN(R) / /

Table 3.1: behavior of machine Mx. ”B” denotes blocking states, ”W” denotes opera-

tional states, and ”R” denotes down states.

of the MLD are function of the output parameters of the BLD. ) they can be obtained.

Therefore, all the transition probabilities in this Markov chain are known and the

unique stationary distribution can be calculated.

Machine Level Analysis. By analyzing the Markov chain in Figure 3.8, the steady-

state probabilities of Mx can be derived (as mentioned earlier, the same procedure is

applied to obtain the steady state probabilities of the Markov chain characterizing the

machine My). Then, the upstream pseudo-machines Mu,x(i), i = 1, 2 is characterized

by approximating the Markov model of Mx steady states. The Markov chain in Figure

3.8 can be solved and the steady-state probabilities can be calculated. Then, in order

to match the simplified multiple failure mode machine structure, the Markov chain of

Figure 3.8 is transformed into the Markov chain of Figure 3.9. The transformation

is made through the re-distribution of the calculated steady-state probabilities, per-

formed by using the following State Aggregation Equations. For Mu,x(1), the following

equations are adopted (3.13 3.14 3.15 3.16):

π (W u,x(1)) = π(W 1W 2

)αx1 + π

(W 1B2

)αx1 (3.13)

46


where π (W u,x(1)) indicates the state in which the Pseudo machine Mu,x(1) is operating

(the original machine is processing sub-assemblies for the buffer Bx1 ). In order to obtain

this state, we need to sum up the portion of the state (W 1W 2) and (W 1B2) that the

machine is processing for Bx1 . It must be notice that in the state (W 1B2) due to the

lack of control on the flow of material, there are some portion of the sub-assemblies

directed to Bx1 , which are discarded consequently. We must consider only αx1 percent

of the state as operational state for Mu,x(1).

π(W̄ u,x(1)

)= π

(W 1W 2

)αx2 + π

(W 1B2

)αx2 (3.14)

The state π(W̄ u,x(1)

)is considered as a failure mode for Mu,x(1), because the original

machine is processing the sub-assemblies for Bx2 . This state can be obtained by adding

up the proportion of the (W 1W 2) state in which the sub-assemblies belong to Bx2

((W 1W 2)αx2) and the proportion of the (W 1B2) state in which the sub-assemblies are

discarded.

π (Bu,x(1)) = π(B1W 2

)+ π

(B1B2

)+ π(B1R2) (3.15)

The blocking state of the Mu,x(1) is the states of the original machine in which the

machine is idle from Mu,x(1) point of view. The (B1W 2) state is completely involved

because even if the original machine processes the sub-assembly for Bx1 , still the sub-

assembly is discarded. The second term of the right hand side, (B1B2), is the state in

which the original machine is idle because both buffers are full, thus from Mu,x(1) point

of view the Pseudo machine is idle as well. The third term, (B1R2) is added because

the original machine is idle from the Mu,x(1) point of view due to the observing full

buffer (Bx1 ).

π (Ru,x(1)) = π(R1B2

)+ π (R) (3.16)

The remaining two state of the Markov chain characterizing the machine Mx represent

the state in which machine is locally failed and they sum up to obtain the down state

of the Mu,x(1).

47


In order to obtain the state probabilities of the Pseudo Mu,x(2), we need to aggregate

the Markovian state of the original machine in a following manner:

π (W u,x(2)) = π(W 1W 2

)αx2 + π

(B1W 2

)αx2 (3.17)

π(W̄ u,x(2)

)= π

(W 1W 2

)αx1 + π

(B1W 2

)αx1 (3.18)

π (Bu,x(2)) = π(W 1B2

)+ π

(B1B2

)+ π(R1B2) (3.19)

π (Ru,x(2)) = π(B1R2

)+ π (R) (3.20)

Inputs to the BLD. Considering the state transition diagram for the pseudo-machine

Mu,x(1) (Figure 3.9), and knowing all the state probabilities, it is possible to obtain

the modified local failures and the competition failure of the Mu,x(1) (the same for the

modified local failure and the competition failure of Mu,x(2)). As mentioned earlier, it

must be noticed that the probability of local failure for the upstream Pseudo machine

is higher than the local failure probability of the original machine. This is because the

machine might fail while processing the sub-assembly which goes to the buffer of the

other quality class, Bx2 .

We can evaluate the local modified failure parameters of the upstream Pseudo machine

by applying the balancing equation on node (Ru,xt (1)) of state transition diagram of

Figure 3.9. Therefore, the probability of Mu,x(1) failing in local mode can be obtained

as:

pu,xt (1) =π (Ru,xt (1))

π (W u,x(1))ru,xt (1) t = 1, .., Tx (3.21)

48


and similarly for Mu,x(2) is given as:

pu,xt (2) =π (Ru,xt (2))

π (W u,x(2))ru,xt (2) t = 1, .., Tx (3.22)

In order to obtain the competition failure parameters of Mu,x(1), we apply the balance

equations on the node W̄ u,x(1), due to the fact that we obtained the probability of

W̄ u,x(1) (that represents the state in which the Pseudo machine Mu,x(1) is not pro-

cessing the sub-assembly because the other Pseudo machine Mu,x(2) is processing a

sub-assembly). Thus, the probabilities of failure and repair for the competition failure

mode of the Mu,x(1) can be derived as follows:

pu,xTx+1(1) =π(W̄ u,x(1)

)π (W u,x(1))

ru,xTx+1(1) (3.23)

ru,xTx+1(1) = αx2(1−Tx∑t=1

pxt )

Similarly for the Mu,x(2), we obtain the following equations for competition repair

and failure parameters:

pu,xTx+1(2) =π(W̄ u,x(2)

)π (W u,x(2))

ru,xTx+1(2) (3.24)

ru,xTx+1(2) = αx2(1−Tx∑t=1

pxt )

3.4.2.2 Assembly Machine

The application of the MLD to the assembly machine Ma is presented in this section.

49


Buffers

Matching flowMachine State Input Buffer Prob.

Bx1 /By

1 Bx2 /By

2

NE E 1 UP(W 1S2) Bx1 /By

1 1

E NE 2 UP(S1W 2) Bx2 /By

2 1

NE NE 1 UP(W 1W 2) Bx1 /By

1 αa1

NE NE 2 UP(W 1W 2) Bx2 /By

2 αa2

E E 1-2 ST(S1S2) / /

NE E 1-2 DOWN(R1S2) / /

E NE 1-2 DOWN(S1R2) / /

NE NE 1-2 DOWN(R) / /

Table 3.2: Behavior of machine Ma. ”S” denotes starvation states, ”W” denotes opera-


State Transition Diagram. Depending on the level of the upstream buffers, ma-

chine Ma behaves as reported in Table 3.2 (where E indicates that one of the two

buffers is empty, NE indicates that none of the buffers is empty).

The Markov chain of original machine (Ma) is characterized by all the possible states

that the machine may observe. For example for each local failure mode a unique state

is associated. However, in order to simplify the picture, in Figure 3.10 the Markov

chain of Ma is illustrating the macro states of the original machine. This means, all the

state of the same type are grouped into a unique aggregated state, without considering

the different failure mode. Each aggregated state is defined by two state indicators,

the first term refers to the first coupled upstream buffers (Bx1 and By

1 ) and the second

refers to the second coupled upstream buffers (Bx2 and By

2 ). Each state indicator can

assume three different states, Starved (S ), Working (W ), and Down (R).

The aggregated states probabilities in steady state are obtained by adding up all the

probabilities of the states of the same type. For example the probability of the ag-

gregated state (R1S2) which indicates the state in which the machine is locally down

while the second flow of the sub-assemblies are starved, is obtained by adding up all

the probabilities of the (RiS2) states over the local failure modes of the machine, i.e.,

50


π(R1B2) =

Tx∑i=1

π(RiB2) (3.25)

The assembly machine is starved for one of the flow i if at least one of the two buffers

Bxi or By

i storing the sub-assemblies x and y is empty. The main difference with the

analysis of the split station Mx is the following. If the assembly station is starved since

at least one buffer related to flow f = 2 is empty, then the part is assembled from flow 1

with probability 1. In fact, in the assembly process there is full control of the selection

process. On the contrary, in the sorting process at machine Mx, the quality class of the

next processed part is dependent only on the process variability and cannot be directly

controlled a priory.

The Markov model describing the behavior of the assembly machine is reported in

Figure 3.10. In the following we describe some characteristics of the Markov chain

representing the Ma behavior,

• If the assembly machine is operating and all the upstream buffers are Non-Empty

(NE ), the Markov chain state is (W 1W 2). When assembly machine selects the

coupled upstream buffers the machine state might fall into (W 1S2) or (S1W 2)

depending on the selected coupled buffers and the level of sub-assemblies in the

selected buffers.

• If the assembly machine is in the state (W 1S2) or (S1W 2) and the machine

locally fails Markov model goes to state (R1S2) or (S1R2), respectively. The

Markov model represent the state in which the assembly machine is failed while

one of the couple buffers is starved. If the starvation of the upstream buffer is

resumed while the machine is not repaired, the Markov model transits to (R).

This means the buffers are all Non-Empty while the machine cannot assemble

due to its local failure.

• The system may go to (W 1W 2) from (R1S2) or (S1R2), if the starvation of the

corresponding coupled buffer is resumed and the machine is repaired.

51


Figure 3.10: Markov model representing Ma characteristics.

Figure 3.11: State transition diagram for downstream Pseudo machine l(x1).

52


• If the machine is in state (W 1S2) or (S1W 2) the assembly machine selects the

available coupled buffers (for example Bx2 and By

2 in case the state is (W 1S2)) with

probability of 1. When the selected coupled buffer become starved (obviously the

machine is operating), the system goes to (S1S2).

As it can be noticed from the Markov chain of assembly machine, the probabilities of

transition to starvation states are unknown and cannot be derived directly from the

original system. However, through the appropriate equations in BLD (see equation

3.11) the unknown parameters of the MLD are function of the output parameters of

the BLD. The other parameters of the Markov model of assembly machine is known.

We need to highlight that the transition probabilities which are composed by the local

failures of the assembly machine, the original local failure parameters are used. Be-

cause the modified local failure parameters are applied to interrupt the flow of material

leaving the buffer for building block evaluation. However in the Markov chain model,

the Markov model is characterizing the assembly machine while considering the four

upstream buffers. Also, for the same reason the competition failures are not applied in

the Markov model of the assembly machine.


state probabilities of Ma can be derived. In order to characterize the downstream

pseudo-machine structure of each building blocks, Md,x(i), i = 1, ..., 4, the Markov

chain of Figure 3.10 is transformed into the Markov chain of Figure 3.11. The transfor-

mation is made through the re-distribution of the calculated steady-state probabilities,

performed by using the following State Aggregation Equations. For Md,x(1), the fol-

lowing equations (equations 3.26, 3.27, 3.28 and 3.29)are adopted:

π(W d,x(1)

)= π

(W 1W 2

)αa1 + π

(W 1S2

)(3.26)

Where π(W d,x(1)

)denotes the state in which the Pseudo machine Md,x(1) is operating

(the original machine is processing sub-assemblies selected from the coupled buffers Bx1

and By1 ). In order to obtain this state, we need to sum up the portion of the state

53


(W 1W 2) in which the assembly machine process the sub-assemblies coupled from Bx1

and By1 , and the total probability of state (W 1S2). It must be notice that in the state

(W 1S2) due to the full control of the flow of material, the assembly machine selects the

first sub-assembly couples and the complete steady state probability is considered.

π(W̄ d,x(1)

)= π

(W 1W 2

)αa2 (3.27)

The π(W̄ d,x(1)

)state is considered as a failure mode for Md,x(1), because the original

assembly machine is processing the sub-assemblies from Bx2 and By

2 while the corre-

sponding coupled buffers are NE. This state can be obtained by considering only the

proportion of the (W 1W 2) state. The assembly machine is able to select the coupled

buffers, in this state the probability of selecting Bx2 and By

2 is αa2.

π(Sd,x(1)

)= π

(S1W 2

)+ π

(S1S2

)+(S1R2

)(3.28)

The starvation state of the Md,x(1) is the states of the assembly machine in which

the machine is idle from Md,x(1) point of view. The (S1W 2) state is considered com-

pletely because of the original machine is starved from Md,x(1) point of view. The

second term of the right hand side, (S1S2), is the state in which the original machine

is idle because both coupled buffers are starved, thus from Md,x(1) point of view the

Pseudo machine is idle as well. The third term, (S1R2) is added because the original

machine is idle from the Md,x(1) point of view due to the starved coupled buffer (Bx1

or By1 or both are empty).

π(Rd,x(1)

)= π

(R1S2

)+ π (R) (3.29)

The remaining two state of the Markov chain of machine Ma represent the state in

54


which machine is locally failed and they are summed up to obtain the local down state

of the Md,x(1).

The aggregated steady state probabilities of the Pseudo machine Md,y(1) is treated in

the same fashion as the Md,x(1).

In order to obtain the state probabilities of the Pseudo Md,x(2), we need to aggregate

the Markovian state of the original machine in a following manner (the same aggregation

is applied for Md,y(2)):

π(W d,x(2)

)= π

(W 1W 2

)αa2 + π

(S1W 2

)(3.30)

π(W̄ d,x(2)

)= π

(W 1W 2

)αa1 (3.31)

π(Sd,x(2)

)= π

(W 1S2

)+ π

(S1S2

)+(R1S2

)(3.32)

π(Rd,x(2)

)= π

(S1R2

)+ π (R) (3.33)

Inputs to the BLD. Considering the steady state probabilities of the state transition

diagram depicted in Figure 3.11 for downstream Pseudo machines Md,x(i), i = 1, ..., 4,

the modified local failure pd,xt (i) and the competition failure and repair parameters

pd,xTx+1(i) and rd,xTx+1(i) can be obtained. Again, the modified local failure of the down-

stream Pseudo machines for each building block must be greater than the local failure

parameters of the original machine. This is because the assembly machine in the origi-

nal system might fail while it is processing the other coupled sub-assemblies. Also, the

failure probabilities of remote failure modes rd,xTa+1+j(i) and pd,xTa+1+j(i), i = 1, ..., 4 and

j = 1, ..., Ty can be derived, to be given in input to the BLD together with modified

local failure and competition failure parameters.

55


In order to obtain the modified local failure parameters of the downstream Pseudo

machine Md,x(1) by applying the balancing equation on node (Rd,xt (1)) of state transi-

tion diagram of Figure 3.11. Therefore, the local failure probability of Md,x(1) can be

obtained as:

pd,x,1t (i) =π(Rd,xi (1)

)π (W d,x(1))

rd,x,1t (i) i = 1, ..., Ta (3.34)

rd,x,1t (i) = ra(i) i = 1, ..., Ta (3.35)

Applying the balance equation on node (W̄ d,x(1)) we can derive the competition failure

parameters as written bellow:

pd,xTx+1(1) =π(W̄ d,x(1)

)π (W d,x(1))

rd,xTx+1(1) (3.36)

rd,xTx+1(1) = αa1(1− P1) when P1 = 1− Pa −Tx+Ty∑k=1

ps,d,1k (3.37)

The remote down states of the Pseudo machine Md,x(1) are those interruptions of flow

due to the empty buffer By1 which cause starvation of the Md,x(1). Thus, the following

can be written:

pd,xTa+1+i(1) = py,s,1i i = 1, ..., Ty (3.38)

rd,xTa+1+i(1) = ry,s,1i i = 1, ..., Ty (3.39)

The same reasoning is applied for the modified local failure, competition failure and the

remote failure and repair parameters of the other three downstream Pseudo machines.

For Md,x(2) the following equations are derived:

pd,x,2t (i) =π(Rd,xi (2)

)π (W d,x(2))

rd,x,2t (i) i = 1, ..., Ta (3.40)

rd,x,2t (i) = ra(i) i = 1, ..., Ta (3.41)

56


Applying the balance equation on node (W̄ d,x(2)) we can derive the competition failure


pd,xTx+1(2) =π(W̄ d,x(2)

)π (W d,x(2))

rd,xTx+1(2) (3.42)

rd,xTx+1(2) = αa2(1− P2) when P2 = 1− Pa −Tx+Ty∑k=1

ps,d,2k (3.43)

The remote down states of the Pseudo machine Md,x(2) are those interruptions of flow

due to the empty buffer By2 which cause starvation of the Md,x(2). Thus, the following

can be written:

pd,xTa+1+i(2) = py,s,2i i = 1, ..., Ty (3.44)

rd,xTa+1+i(2) = ry,s,2i i = 1, ..., Ty (3.45)

The failure and repair parameters of Md,y(1) are obtained as following:

pd,y,1t (i) =π(Rd,yi (1)

)π (W d,y(1))

rd,y,1t (i) i = 1, ..., Ta (3.46)

rd,y,1t (i) = ra(i) i = 1, ..., Ta (3.47)

Applying the balance equation on node (W̄ d,y(1)) we can derive the competition failure


pd,yTx+1(1) =π(W̄ d,y(1)

)π (W d,y(1))

rd,yTx+1(1) (3.48)

rd,yTx+1(1) = αa1(1− P1) when P1 = 1− Pa −Tx+Ty∑k=1

ps,d,1k (3.49)

The remote down states of the Pseudo machine Md,y(1) are those interruptions of flow

due to the empty buffer Bx1 which cause starvation of the Md,y(1). Thus, the following

57


can be written:

pd,yTa+1+i(1) = py,s,1i i = 1, ..., Tx (3.50)

rd,yTa+1+i(1) = rx,s,1i i = 1, ..., Tx (3.51)

The failure and repair parameters of Md,y(2) are obtained as following:

pd,y,2t (i) =π(Rd,yi (2)

)π (W d,y(2))

rd,y,2t (i) i = 1, ..., Ta (3.52)

rd,y,2t (i) = ra(i) i = 1, ..., Ta (3.53)

Applying the balance equation on node (W̄ d,y(2)) we can derive the competition failure


pd,yTx+1(2) =π(W̄ d,y(2)

)π (W d,y(2))

rd,yTx+1(2) (3.54)

rd,yTx+1(2) = αa1(1− P1) when P1 = 1− Pa −Tx+Ty∑k=1

ps,d,2k (3.55)

The remote down states of the Pseudo machine Md,y(2) are those interruptions of flow

due to the empty buffer Bx2 which cause starvation of the Md,y(2). Thus, the following

can be written:

pd,yTa+1+i(2) = py,s,2i i = 1, ..., Tx (3.56)

rd,yTa+1+i(2) = rx,s,2i i = 1, ..., Tx (3.57)

3.4.3 Algorithm

In this section we describe the details of the iterative algorithm applied to develop

the performance evaluation tool. The method is implemented in C++ and in the

next section we will illustrate the accuracy and reliability of the tool. The proposed

58


decomposition equations are solved by following an iterative algorithm inspired by DDX

algorithm that updates in sequence the parameters of the upstream and the downstream

pseudo-machines, by alternately visiting the MLD and the BLD.

1.initialization: For each Pseudo machine of each building block the local failures

are initialized to the values of the machines of the original system, while the remote

parameters and competition failure and repair probabilities are initialized to small

value, 0.05.

• For building block Mu,x(j) and Md,x(j), j=1,2

pu,xi (j) = pxi pu,xTx+1(j) = 0.05 i = 1, ..., Tx

ru,xi (j) = rxi ru,xTx+1(j) = 0.05 i = 1, ..., Tx (3.58)

pd,xi (j) = pai pu,xTa+1(j) = 0.05 i = 1, ..., Ta j = 1, 2

pd,xTa+1+k(j) = 0.05 k = 1, ..., Ty j = 1, 2

rd,xi (j) = rai ru,xTa+1(j) = 0.05 j = 1, 2

• For building block Mu,y(j) and Md,y(j), j=1,2

pu,yi (j) = pyi pd,yTy+1(j) = 0.05 i = 1, ..., Ty

ru,yi (j) = ryi rd,yTy+1(j) = 0.05 i = 1, ..., Ty

59


pd,yi (j) = pai pd,yTx+1(j) = 0.05 i = 1, ..., Ta j = 1, 2

pd,yTa+1+k(j) = 0.05 k = 1, ..., Tx j = 1, 2

rd,yi (j) = rai rd,yTx+1(j) = 0.05 j = 1, 2

Step 1 : Each building block is evaluated with the parameters updated in the previous

iteration (in the first iteration the initialized parameters all applied). Probabilities of

starvation, blocking and the average throughput of each building block is obtained with

the method proposed in Tolio et al. [2002]. Transition probabilities of the MLD for each

dedicated Markov model is updated referring to equations 3.10 and 3.11.

Step 2 : The failure parameters of Upstream Pseudo Machines and the Downstream

Pseudo Machines are evaluated as follows:

• Evaluation of steady state distribution of Markov model of manufacturing ma-

chines of the original system, Mx and My and the assembly machine Ma by

solving the linear equations of the discrete state-discrete time dedicated Markov

chains. The parameters for transition probabilities are taken from the results of

the building block evaluations in step 1.

• Aggregation of the states for two Pseudo machine Markov models, according to

equations 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, 3.19 and 3.20 for upstream Pseudo

machines and 3.26, 3.27, 3.28, 3.29, 3.30, 3.31, 3.32 and 3.33 for down stream

Pseudo machines.

• Evaluation of modified local failures for upstream Pseudo machines of building

blocks representing the original machine Mx using equation 3.21 and for upstream

Pseudo machines of building blocks representing the original machine My using

equation 3.22 .

• Evaluation of modified local failures for downstream Pseudo machines of building

blocks representing the original machine Ma using equation 3.34.

60

3.5. NUMERICAL RESULTS

• Evaluation of remote failures of the downstream Pseudo machines for each build-

ing block using equations 3.38.

• Evaluation of competition failures of upstream Pseudo machines using equations

3.23 and 3.24 and for downstream pseudo machines by applying 3.36, 3.42, 3.48,

3.54.

• Substitution of failure and repair parameters (modified local failure, competition

failure and remote failure) to the step 1 for each building block.

The algorithm terminates when the conservation of flow condition becomes true:

| THx(i)− THy(i) |≤ ε for i = 1, 2

3.4.4 System Performance Measures

Following the algorithm, upon convergence, the system performance can be calculated

as:

THTot =

F∑i=1

THx(i) =

F∑i=1

THy(i);

Yi = (1− γai ) ∀i = 1, .., F

THEff =

F∑i=1

THx(i) · Yi;

Y System =THEff

THTot;

n̄xi = n̄x(i); n̄yi = n̄y(i); WIP =F∑i=1

n̄xi + n̄yi ;

3.5 Numerical Results

3.5.1 Accuracy testing

The accuracy of the proposed approximate analytical method is tested by comparing

the results with those provided by a Discrete Event Simulation (DES) model. The

61


simulation model is developed under the same manufacturing system assumptions. In

order to do so, we developed a DES model where the behavior of the machines is sim-

ulated under realistic system setting.

In order to characterize the simulation model, the sub-assembly key quality charac-

teristic measurements are sampled from the population distributions and are assigned

as attributes to the entities. Then, the sub-assemblies are sorted according to adopted

partitioning policy. After the component matching, the key quality characteristics

value of the assembled product is calculated and the non-conforming final assemblies

are identified and tagged by comparing this value with the predefined specification lim-

its. In this way, conforming final assemblies and non-conforming final assemblies in the

output flows are characterized and the generic system performance measures can be

estimated after a simulation run. In order to avoid the deadlock, the discard rule have

been taken into consideration as it was considered for the analytical model.

With R simulation replicates, the percentage error of the analytical method in the

estimation of the generic system performance measure, τ , versus simulation is estimated

by using the following equations:

τ̂Simulation =

∑Rr=1 τ

Simulationr

R(3.51)

ε(τ) =(τ̂Simulation − τanalytical)

τ̂Simulation

Given the large number of variables characterizing the considered problem, and the

consequent wide set of possible system configurations to be tested, we focus the nu-

merical analysis only on a sub-set of system configurations, that are representative of

the entire class of systems. The set of fixed parameters describing the analyzed system

configurations are reported in Table 3.3. The number of quality classes is set to C=2,

the consequent number of buffers is therefore F=2, equal width partitioning scheme for

sorting of sub-assemblies are adopted.

Regarding the assembly station, the quality characteristics of the assembled product

is the gap between components X and Y, i.e. z = x − y. The matching policy is

62

3.5. NUMERICAL RESULTS

Mx My Ma

X ∼ N(µx, σ2x) Y ∼ N(µy, σ

2y) Z = X − Y ; Z ∼ N(µx − µy, σ

2x + σ2

y)

µx=4; σx=0.116 µy=3.3; σy=0.05 µz=0.7; σz=0.126

LSLx=3.5 USLx=4.5 LSLy=2.8 USLy=3.8 LSLz=0.61 USLz=0.79

αx1=0.5 αx

2=0.5 αy1=0.5 αy

2=0.5 αa1 , αa

2 : factors

γx ≈ 0 γy ≈ 0

γ ≈ 0.4761 if F = 1,

γ1 = γ2 ≈ 0.2881 if F = 2

px, rx: factors py = 0, 01; ry = 0, 05 pa, ra: factors

Table 3.3: Summary of the adopted parameters.

a one-to-one matching between coupled buffers containing sub-assemblies X and Y.

The assembly policy is probabilistic depending on the available sub-assemblies in set of

coupled buffers. The reliability parameters of the manufacturing machine processing

component Y, My are fixed, while the reliability parameters of the other machines will

be modified to test systems with different bottleneck locations.

In order to generate different configurations to be tested, we adopted a Midpoint Latin

Hypercube Design approach, MLHD(80,9) with 9 factors and 80 runs. The ranges of

variability of the design factors are reported in Table 3.4. After generation of these

randomized 80 runs, we evaluate the performance of the system configurations with the

DES model and with the analytical method. Within the DES model, for each experi-

mental point we executed R=10 replicates of 1000000 time units with 100000 units of

warm up time, where the system statistics are not collected. The response of major

interest is the relative error of the analytical method towards simulation in the estima-

tion of the effective throughput and in the estimation of the total WIP. Therefore, for

each experimental point, two responses are obtained.

Parameter N1x N2

x N1y N2

y px rx pa ra α1a

Lower Bound 3 3 3 3 0.01 0.03 0.01 0.03 0.2

Upper Bound 30 30 30 30 0.1 0.3 0.1 0.3 0.8

Table 3.4: Range of variable parameters of accuracy test of analytical tool.

63


The results of this experimental plan are reported in Table 3.5. The method well cap-

tures the real system dynamics providing good estimates of the effective production

rate of the system.

In details, the average error of effective throughput over the 80 test cases is 1.07%, while

in the 90% of cases the error is below 3%. The method is accurate also while evaluating

the total WIP, with average estimation errors below 6% . It is worth to mention that

while the simulation requires about 8 hours to evaluate the 80 test systems the proposed

method requires 5 minutes for the entire experimental plan.

64

3.5

.N

UM

ER

ICA

LR

ES

ULT

S

ID Nx1 Nx

2 Ny1 Ny

2 px rx pa ra αa1 EEff

Sim EEffMet |ε%| WIPSim WIPMet |ε%|

1 7 13 10 25 0,077 0,275 0,063 0,258 0,459 0,50 0,51 2,03 13,57 12,77 -5,87

2 15 22 24 9 0,076 0,146 0,044 0,295 0,489 0,46 0,47 0,89 23,81 24,20 1,65

3 14 28 27 6 0,040 0,038 0,016 0,089 0,744 0,34 0,34 -0,32 29,08 31,12 7,02

4 18 28 24 26 0,014 0,187 0,012 0,062 0,391 0,55 0,52 -5,10 42,86 45,48 6,10

5 25 24 15 21 0,060 0,092 0,054 0,163 0,264 0,42 0,43 1,20 21,19 20,10 -5,16

6 22 12 29 4 0,023 0,157 0,032 0,254 0,354 0,55 0,56 1,77 28,26 27,11 -4,06

7 28 23 10 29 0,071 0,214 0,036 0,160 0,624 0,51 0,47 -8,24 22,36 21,22 -5,09

8 4 9 20 18 0,057 0,180 0,034 0,140 0,691 0,48 0,48 -0,60 18,69 18,77 0,41

9 9 9 30 19 0,027 0,170 0,022 0,170 0,759 0,55 0,56 1,82 19,15 20,11 4,99

10 15 11 10 21 0,094 0,140 0,041 0,076 0,339 0,38 0,38 -0,34 16,94 17,72 4,61

11 30 10 9 25 0,075 0,099 0,074 0,079 0,654 0,33 0,33 1,63 47,44 44,43 -6,35

12 24 19 29 27 0,089 0,133 0,025 0,268 0,571 0,42 0,42 -1,10 47,33 44,22 -6,57

13 14 7 5 14 0,016 0,035 0,070 0,200 0,406 0,40 0,41 3,49 23,03 22,20 -3,61

14 12 26 13 6 0,024 0,184 0,048 0,099 0,496 0,44 0,46 2,54 42,83 39,41 -7,99

15 5 24 21 24 0,072 0,292 0,045 0,265 0,474 0,53 0,54 1,87 33,56 30,24 -9,89

16 23 29 8 12 0,068 0,069 0,023 0,038 0,601 0,33 0,33 -1,30 30,45 27,26 -10,49

17 16 16 22 26 0,078 0,052 0,024 0,153 0,646 0,28 0,28 0,34 44,85 44,65 -0,45

18 8 21 25 13 0,053 0,268 0,067 0,234 0,361 0,51 0,53 3,02 37,65 34,52 -8,30

19 13 27 17 26 0,042 0,103 0,031 0,116 0,249 0,47 0,47 1,76 37,63 35,35 -6,06

20 8 18 22 8 0,062 0,032 0,061 0,133 0,669 0,23 0,23 0,99 30,47 29,26 -3,97

21 23 13 25 6 0,081 0,241 0,090 0,180 0,399 0,45 0,46 1,87 43,97 40,09 -8,81

22 12 30 9 29 0,066 0,082 0,075 0,281 0,661 0,39 0,39 0,75 35,59 33,94 -4,62

23 29 5 21 5 0,056 0,265 0,071 0,244 0,309 0,50 0,51 1,66 33,65 28,74 -14,58

24 4 14 6 22 0,032 0,065 0,093 0,055 0,256 0,24 0,25 2,79 35,53 34,60 -2,64

25 26 30 19 24 0,069 0,130 0,078 0,103 0,721 0,39 0,40 2,13 64,21 62,22 -3,09

26 19 15 27 16 0,036 0,173 0,065 0,130 0,714 0,45 0,47 2,84 47,22 45,25 -4,17

27 17 14 29 14 0,059 0,167 0,092 0,261 0,796 0,47 0,49 2,79 38,51 37,25 -3,27

65

3.

SE

LE

CT

IVE

AS

SE

MB

LY

SY

ST

EM

CO

NV

EN

TIO

NS

,S

YS

TE

MD

ES

CR

IPT

ION

AN

DA

NA

LY

TIC

AL

PE

RF

OR

MA

NC

EE

VA

LU

AT

ION

ME

TH

OD

OL

OG

Y

28 20 8 17 30 0,090 0,204 0,014 0,143 0,699 0,48 0,47 -2,30 36,93 33,33 -9,76

29 22 28 11 14 0,080 0,194 0,030 0,096 0,226 0,46 0,47 1,82 31,71 27,53 -13,18

30 7 10 23 17 0,093 0,136 0,098 0,197 0,534 0,39 0,39 1,23 38,68 36,90 -4,60

31 28 15 28 7 0,097 0,079 0,077 0,167 0,789 0,31 0,31 1,10 35,30 34,30 -2,85

32 4 27 18 12 0,079 0,221 0,052 0,285 0,504 0,49 0,49 1,33 26,80 24,21 -9,65

33 11 17 30 12 0,011 0,096 0,072 0,298 0,706 0,52 0,54 3,92 35,39 31,19 -11,88

34 8 20 8 29 0,012 0,197 0,043 0,248 0,241 0,53 0,55 2,84 25,34 23,35 -7,87

35 29 19 6 10 0,020 0,258 0,039 0,224 0,774 0,54 0,55 2,37 42,97 40,92 -4,77

36 6 23 12 11 0,029 0,062 0,027 0,241 0,736 0,46 0,46 1,22 21,07 18,58 -11,83

37 19 4 14 15 0,013 0,295 0,040 0,292 0,564 0,55 0,57 2,46 27,36 24,74 -9,55

38 20 18 16 23 0,041 0,045 0,013 0,042 0,436 0,35 0,35 -0,39 38,78 36,52 -5,84

39 20 5 13 7 0,035 0,251 0,051 0,113 0,376 0,45 0,46 1,99 30,68 27,42 -10,65

40 27 26 23 28 0,058 0,254 0,035 0,032 0,631 0,33 0,34 0,69 85,80 82,22 -4,18

41 5 15 5 5 0,095 0,059 0,096 0,251 0,211 0,25 0,26 2,16 10,39 9,82 -5,47

42 26 26 15 17 0,031 0,160 0,060 0,177 0,384 0,50 0,52 3,47 53,16 48,33 -9,08

43 16 12 12 4 0,033 0,285 0,085 0,126 0,729 0,39 0,41 4,17 30,72 29,60 -3,63

44 21 19 13 25 0,084 0,119 0,042 0,092 0,541 0,40 0,40 -0,29 41,25 38,09 -7,66

45 9 29 6 23 0,034 0,238 0,049 0,187 0,451 0,51 0,53 3,16 36,32 33,32 -8,26

46 17 5 21 9 0,021 0,177 0,080 0,106 0,481 0,39 0,40 1,87 40,07 37,61 -6,15

47 22 6 11 22 0,054 0,231 0,099 0,052 0,369 0,24 0,24 0,32 54,93 54,11 -1,49

48 30 4 7 20 0,083 0,234 0,056 0,065 0,751 0,35 0,36 1,78 44,46 43,19 -2,86

49 13 22 4 27 0,038 0,055 0,089 0,049 0,766 0,24 0,24 -0,08 53,79 51,46 -4,33

50 6 20 11 20 0,067 0,113 0,076 0,136 0,519 0,39 0,39 0,85 33,38 30,81 -7,71

51 5 8 20 30 0,063 0,200 0,062 0,072 0,781 0,36 0,36 -0,42 50,32 48,55 -3,51

52 19 25 27 15 0,045 0,150 0,095 0,146 0,444 0,42 0,43 1,25 65,28 62,07 -4,92

53 25 20 4 13 0,050 0,298 0,079 0,288 0,429 0,50 0,51 3,51 40,91 37,12 -9,25

54 21 6 28 18 0,098 0,217 0,094 0,123 0,324 0,39 0,39 0,29 54,10 51,35 -5,08

55 12 6 7 11 0,017 0,163 0,068 0,069 0,316 0,34 0,35 2,38 27,73 26,50 -4,42

66

3.5

.N

UM

ER

ICA

LR

ES

ULT

S

56 29 10 26 30 0,030 0,116 0,038 0,190 0,684 0,52 0,49 -5,81 44,28 40,34 -8,89

57 16 25 25 18 0,044 0,106 0,053 0,271 0,639 0,49 0,50 1,28 37,51 34,03 -9,28

58 30 7 28 11 0,061 0,271 0,088 0,119 0,526 0,40 0,41 1,62 59,77 56,24 -5,92

59 6 11 7 16 0,088 0,143 0,011 0,035 0,676 0,38 0,37 -3,19 21,08 20,34 -3,50

60 9 12 18 23 0,049 0,244 0,021 0,086 0,511 0,51 0,52 0,91 33,28 29,27 -12,03

61 23 7 15 15 0,043 0,072 0,050 0,059 0,549 0,34 0,34 0,83 39,40 35,94 -8,78

62 28 27 8 8 0,074 0,261 0,057 0,238 0,331 0,50 0,52 3,60 37,34 31,32 -16,13

63 24 23 20 28 0,048 0,042 0,015 0,150 0,579 0,33 0,33 -0,43 42,94 42,57 -0,87

64 11 24 22 20 0,085 0,278 0,069 0,214 0,286 0,49 0,51 2,38 38,22 35,42 -7,33

65 7 21 9 13 0,047 0,281 0,087 0,221 0,234 0,46 0,48 4,22 26,63 24,91 -6,45

66 27 17 19 10 0,052 0,153 0,017 0,194 0,616 0,51 0,52 1,61 24,80 21,70 -12,50

67 24 14 30 10 0,051 0,076 0,047 0,204 0,586 0,41 0,42 0,97 36,79 34,80 -5,41

68 10 22 16 19 0,025 0,086 0,033 0,278 0,346 0,51 0,53 2,33 27,35 23,87 -12,74

69 10 8 23 16 0,018 0,207 0,097 0,211 0,414 0,47 0,48 2,33 40,48 38,23 -5,56

70 11 11 16 24 0,015 0,248 0,066 0,275 0,594 0,54 0,56 3,38 35,92 31,91 -11,16

71 27 4 4 5 0,092 0,049 0,029 0,157 0,556 0,23 0,22 -6,18 9,03 8,22 -9,00

72 26 29 12 27 0,026 0,224 0,020 0,082 0,279 0,52 0,54 2,80 49,86 45,84 -8,07

73 18 30 26 22 0,086 0,288 0,059 0,045 0,301 0,31 0,31 0,94 79,35 77,94 -1,78

74 18 9 14 7 0,070 0,123 0,081 0,227 0,204 0,42 0,43 1,42 22,78 20,90 -8,23

75 10 16 5 28 0,087 0,190 0,084 0,109 0,421 0,38 0,38 1,39 40,46 38,25 -5,44

76 21 21 18 9 0,096 0,126 0,083 0,217 0,466 0,40 0,40 1,05 28,71 25,85 -9,95

77 25 13 14 21 0,022 0,089 0,026 0,207 0,294 0,53 0,55 2,26 31,76 30,22 -4,86

78 13 25 24 19 0,039 0,227 0,058 0,184 0,609 0,51 0,53 2,59 51,01 46,40 -9,04

79 14 18 19 8 0,099 0,211 0,086 0,231 0,219 0,45 0,46 1,89 28,76 26,66 -7,29

80 15 16 26 4 0,065 0,109 0,018 0,173 0,271 0,44 0,44 1,03 27,43 26,22 -4,41

Table 3.5: experimental results.

67


68

4


Analysis

4.1 Selective Assembly System Behavior

Given the good accuracy of the proposed approach, the method has been used to study

the system behavior of the selective assembly systems. In detail, two sets of experiments

have been conducted. First, the impact of the total buffer size on the total throughput,

effective throughput and WIP of the selective assembly system of two quality classes

is explored and the results are compared to those of the normal assembly system with

the same total buffer space. This experiment leads us to realize the benefits of the se-

lective assembly system comparing to the normal assembly system. Second, we studied

the behavior of the selective assembly system performance under increased number of

quality classes. Again in the second experiment, the total buffer size of the system is

fixed as the number of quality classes increases.

For both experiments, the same data as the previous experiments are considered, except

the machines reliability data. They are all set equal to the machine of the previous set

of tests (p = 0.01, r = 0.05). For the first experiment, since the reliability parameters

are identical, the total buffer space is equally distributed between the buffers in the

system. This is the best possible way to allocate buffers when the machines are iden-

tical. The total buffer size varies from 12 to 60, which means for each buffer the size

varies from 3 to 15 (N ix and N i

y for i = 1, 2). For the second experiment, we considered

69

4. SELECTIVE ASSEMBLY SYSTEM ANALYSIS

the same total buffer space, 60, and we divide the total space by the number of quality

classes as it increases form 2 to 6.

Although the selective assembly system provides a higher system yield with respect

to the non-selective assembly system (from 52% to 71% which is approximately 36%

improvement), but it affects negatively the total throughput. As it is shown in Figure

4.1, the total throughput of the system is increasing in both normal assembly and se-

lective assembly systems as the total buffer space increases. But, due to the logistic

complexity of the selective assembly system the total throughput of this system is re-

duced compared to the non-selective assembly system. It is important to notice that,

because of the considered deadlock avoidance policy, discard policy, there are fraction

of manufactured sub-assemblies which are neglected by the manufacturing machines

and this leads to decreased total throughput. But, as it can be observed in the Figure

4.1, the negative effect of selective assembly system on the total throughput become

less evident as the total buffer space increases.

The combined result of increased yield and decreased total throughput is an increase of

the effective throughput with respect to the traditional, non-selective, assembly system,

as represented in Figure 4.2. This is because the weight of the increased yield is more

than the negative weight of the total throughput. In addition, the positive effect of

the selective assembly system on the effective throughput of the system is even more

visible as the total buffer size increases. For example, when the total buffer size is 12,

the effective throughput improvement comparing to the traditional assembly system is

18.17% while the improvement is 28.68% when the total buffer size increases to the 60.

Therefore, as the effective throughput is the performance measure which effectively il-

lustrate the benefits of one system comparing to the other, we can notice the remarkable

improvement of the selective assembly system comparing to the non-selective assembly

system.

Another result is the fact that the selective assembly system entails an average inventory

level increase comparing to the non-selective assembly system, as depicted in Figure

4.3. As mentioned earlier, the selective assembly system translates the system quality

issue into logistic performance issue. In fact, the price of more effective throughput is

70

4.1. SELECTIVE ASSEMBLY SYSTEM BEHAVIOR

Figure 4.1: Total throughput behavior as the total buffer space increases.

71


Figure 4.2: Effective throughput behavior as the total buffer space increases.

72

4.2. THE EFFECT OF MORE QUALITY CLASSES FOR SELECTIVEASSEMBLY SYSTEMS

Figure 4.3: WIP behavior as the total buffer size increases.

paid by the more average system work in progress. The increased WIP is more evident

as the total buffer space is increased.

4.2 The Effect of More Quality Classes for Selective As-

sembly Systems

In this thesis the analytical performance evaluation tool is provided for two quality

classes and the accuracy of the tool is tested comparing to simulation results of the

same configuration model. The extension of the analytical model of two quality class

model to more quality classes is straightforward with the same provided framework.

But we applied the developed discrete event simulation model to analyze the selective

assembly systems under more quality classes. In details, we studied the effect of the

number of quality classes on the system yield, the total throughput, and the effective

throughput.

73


Mx My Ma


2y) Z = X − Y ; Z ∼ N(µx − µy, σ

2x + σ2

y)

µx=4; σx=0.116 µy=3.3; σy=0.05 µz=0.7; σz=0.126


px = 0, 01; rx = 0, 05 py = 0, 01; ry = 0, 05 px = 0, 01; rx = 0, 05

Table 4.1: Summary of the adopted parameters for more quality classes test.

The complexity of the selective assembly logistic system increases by the increase in

number of quality classes, but the yield is expected to increase at the same time. The

increased logistic system complexity leads to degraded productivity of the system, re-

sulting in decreased total throughput. On the other hand, the more quality classes im-

proves the final assembly quality because the sub-assemblies are categorized in tighter

quality classes respecting their key quality characteristics. It must be noticed that, the

interaction effect of yield and total throughput is observed as the effective throughput,

which is the supporting performance measure of system management decision making

process.

The machine reliability parameters for this set of experiments are presented in Table 4.1

together with the distributions of key quality characteristics of sub-assemblies. Since

the reliability parameters are identical, the total buffer space of 60 is equally distributed

between the buffers in the system. This is the most effective way to allocate buffers

when the machines are identical.

For more than two quality classes of selective assembly systems we must take into con-

sideration a specific partition scheme. As mentioned earlier, There are two type of

partitioning scheme, the equal width and the equal probability scheme. For this partic-

ular system study we have considered the equal probability scheme. Equal probability

provides the better system performance in terms of productivity due to the lower level

of surplus sub-assemblies when the distribution variations are dissimilar, as discussed

earlier. The detailed partitioning for quality classes (from 2 classes to 6 classes) is

provided in Table 4.2.

74


Sub-Assembly

X Y

Number of Quality Classes Limits LSL USL LSL USL

2Class 1 3,5 4 2,8 3,3

Class 2 4 4,5 3,3 3,8

3

Class 1 3,5 3,950036 2,8 3,278464

Class 2 3,950036 4,049964 3,278464 3,321536

Class 3 4,049964 4,5 3,321536 3,8

4

Class 1 3,5 3,921759 2,8 3,266276

Class 2 3,921759 4 3,266276 3,3

Class 3 4 4,078241 3,3 3,333724

Class 4 4,078241 4,5 3,333724 3,8

5

Class 1 3,5 3,902372 2,8 3,257919

Class 2 3,902372 3,970612 3,257919 3,287333

Class 3 3,970612 4,029388 3,287333 3,312667

Class 4 4,029388 4,097628 3,312667 3,342081

Class 5 4,097628 4,5 3,342081 3,8

6

Class 1 3,5 3,887779 2,8 3,251629

Class 2 3,887779 3,950036 3,251629 3,278464

Class 3 3,950036 4 3,278464 3,3

Class 4 4 4,049964 3,3 3,321536

Class 5 4,049964 4,112221 3,321536 3,348371

Class 6 4,112221 4,5 3,348371 3,8

Table 4.2: Partitioning limits for equal probability scheme.

Table 4.3 provides the performance measures of the interest for the selective assembly

system of 1 class (which represents the normal assembly) to 6 classes. For the nor-

mal assembly system and the selective assembly system of two quality classes, we have

applied our analytical method, while the results of the selective assembly of 3 quality

classes to 6 quality classes, are provided by running the developed simulation model

for 10 replicates of approximately 10000000 time units of operation. 95% confidence

interval widths are 0.01% , 0.01%, and 1.7% of the average effective throughput, aver-

age total throughput and the WIP, respectively.

75


Figure 4.4: Total TH behavior as the number of quality classes increases.

In the Figure 4.4 we illustrate the effect of increasing the number of quality classes on

the total throughput, as the total buffer space is fixed. As it is shown, the increasing

number of quality classes decreases the total throughput (the production rate of both

conforming and non-conforming sub-assemblies). This behavior is due to the additional

imposed complexity to logistic systems as the number of quality classes increases. In

the other words, the material flow complexity is increased by the number of quality

classes. This is because, the upstream manufacturing machines are regulating to place

the processed sub-assemblies into more buffers comparing to the less quality classes.

In fact, the more quality classes to distribute the processed sub-assemblies cause the

lower average buffer level for each sub-assembly in the particular buffer. From the

other hand, the assembly machine only selects the sub-assemblies from the available

coupled buffers. Therefore, the assembly machine remains starved more frequently as

the number of quality classes increases. This causes the lower level of total throughput.

76


For example, the total throughput of the designed selective assembly system with 6

quality classes are reduced comparing to the 2 quality classes by approximately 18%.

Number Of Classes TH-Total TH-Eff Yield

1 0,68 0,36 0,52

2 0,65 0,46 0,71

3 0,62 0,48 0,77

4 0,59 0,47 0,80

5 0,56 0,46 0,82

6 0,55 0,46 0,83

Table 4.3: Performance measures as the number number of quality classes increases.

Although the total throughput is reduced by the number of quality classes, the system

yield is increased as shown in Figure 4.6, as the number of quality classes increases. As a

result of this competing effect, the effective throughput curve is concave, it is increasing

until a certain point and then it starts decreasing (as it is shown in Figure 4.5). Thus,

being concern with the concave behavior of the effective throughput curve, it illustrates

that there is an optimal point to select for the number of quality classes. Therefore,

in order to make a proper decision for design of selective assembly systems in terms

of number of quality classes, there is an absolute need to observe the trad-off between

the logistic complexity and the system yield through the resulting effective throughput.

As mentioned in the previous chapter, the deadlock state is a consequence of system

complexity. In order to avoid the deadlock state, we have considered the discard policy,

both in our analytical method for two quality classes and in the simulation model of

more quality classes. In discard policy, when the manufacturing machines face a full

downstream buffer, they continue the production and if the sub-assembly belongs to the

full buffer it will be discarded. In the other words, discard policy avoids the deadlock

state by imposing the cost of neglecting conforming sub-assemblies. In our model,

both analytical model of two class system and the simulation models for extended

classes, we have considered the discard policy. Although selective assembly systems are

introduced to increase the quality of final assembly at the reduced cost, but discarding

the conforming sub-assemblies seems not economical for the practitioner. Therefore,

77


Figure 4.5: The effective throughput behavior as the number of quality classes increases.

we have introduced the new analytical approach to reduce the discard rate by applying

the process adaptation. In the next chapter we will describe the proposed method in

addition to other new flow control policies to design more efficiently selective assembly

systems for practitioners.

78


Figure 4.6: System Yield behavior as the number of quality classes increases.

79


80

5

Selective and Adaptive Assembly

Systems

5.1 Selective and Adaptive Assembly Systems Definition

Selective and Adaptive Assembly Systems are considered a different approach to im-

prove the quality of the assembled product. The selective part of Selective and Adaptive

Assembly Systems is characterized by the assembly of sub-assemblies based on match-

ing predetermined classification groups as introduced earlier. While the adaptive part

of selective and adaptive assembly systems is characterized by the control of process

parameters in the upstream component manufacturing processes. In fact, in Selective

and Adaptive Assembly Systems the term ”Adaptive” refers to the adaptation of the

target nominal value of the sub-assembly’s key quality characteristic in the upstream

sub-assembly manufacturing processes. This term is denoted as “process mean shift” as

well. By applying these principles, Selective and Adaptive Assembly Systems support

the assembly of high precision products from relatively low precision sub-assemblies, at

the cost of increasing the system complexity and decreasing the logistic performance of

the system.

There are studies that investigate the effects of the adaptability of processes on the

performance of Selective and Adaptive Assembly Systems, in addition to selective

assembly. Selective and Adaptive Assembly Systems productivity simulation results

Herrmann et al. [2010] give insight regarding the inter-dependencies of logistic system

81

5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS

design, production system design, and product design in determining the overall effi-

ciency of selective and adaptive assembly systems.

In Matsuura and Shinozaki [2011a] a one-shift process mean design for selective and

adaptive assembly systems was proposed. In details, by producing the component at

different target process means, each one having an assigned probability, the original

key characteristic distribution of the component was changed and controlled. The

authors show that with one shift in the process mean and the equal-probability par-

titioning scheme, zero surplus components can be obtained at the cost of highly in-

creasing the number of bins. The authors discussed the problem of determining the

optimal mean shift (the adaptation magnitude and frequency) for both equal width and

equal probability partitioning schemes when the sub-assembly with smaller variance is

manufactured at two shifted means and a tolerance constraint on the clearance is given.

The effects of mean shift on manufacturing mating components and the selection of

the number of bins in selective assembly through Taguchi loss function have also re-

ceived attention Kannan et al. [2008]. For the analysis of component tolerances it is

concluded that very lowest possible clearance variation with the loss function of zero

can be achieved when the mating sub-assembly tolerances are equal.

In Matsuura and Shinozaki [2011b], three-shifts process mean designs were investigated

to reduce the number of surplus components, as shown in Figure 5.1, where the process

adaptation is applied to the process of sub-assembly manufacturing with smaller varia-

tion level. In their paper, author proposed an optimal manufacturing mean design that

minimizes the number of surplus components when equal width partitioning scheme

has been applied. They demonstrated that the use of the proposed optimal process

mean shift design significantly reduces the number of surplus components compared

with the no-shift design.

When there is a large difference between the process variation of two sub-assemblies,

equal width partitioning will result in a large number of surplus sub-assemblies and

equal probability partitioning will result in some rejected products due to the improper

partitioning width design. In Matsuura and Shinozaki [2011a] authors proposed a

82

5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION

Figure 5.1: Three shift policy for adaptive production systems.

method to determine the optimal process mean shift for both equal width and equal

probability in such a way that the surplus sub-assemblies are minimized. They have

shown that in some cases it is possible to achieve the zero level of surplus sub-assemblies

under equal probability partitioning scheme, with the cost of increased number of par-

titioning classes compare to the equal width partitioning scheme. Authors in Kannan

and Jayabalan [2002] and Kannan et al. [1997] proposed a method of manufacturing

components with smaller process variation at several shifted means. In Matsuura and

Shinozaki [2011a] they have shown their method is out-performing the method pro-

posed in Kannan and Jayabalan [2002].

As discussed above, although the process adaptability of selective and adaptive as-

sembly systems has been proposed as a suitable solution to improve the system per-

formance, the optimal number of process mean adjustment to minimize the surplus

sub-assemblies have not being considered. Furthermore, the effect of optimal adapt-

ability policies on the overall system performance of selective and adaptive assembly

systems received a limited attention. This is important because the effect of surplus

reduction (through several proposed models) need to be analyzed while the policy is

applied in the system with real settings, i.e., unreliable machines and limited buffers.

This is because, the surplus sub-assemblies are those who accumulate in limited capac-

ity buffers and cause the blocking phenomena for the manufacturing machines. This

83


phenomena has been neglected in the previous works by considering the unlimited

buffer capacities that are impractical in real system settings. In the other words, the

importance of the surplus sub-assemblies is underestimated by considering it as the

sub-assemblies which are left with no coupled sub-assemblies, while the main negative

effect is the cause to blocking phenomena. Consequently, it is derived that the surplus

sub-assemblies are the main drive for deadlock phenomenon and the the consequent

discarded sub-assemblies.

As mentioned above, the process mean adjustment might improve the system perfor-

mance by reducing the surplus sub-assemblies. But, process adaptability can be applied

to reduce the discard rate of sub-assemblies in deadlock states as well. As we have men-

tioned in previous chapter, we have applied the discard policy to avoid the deadlock

state for developing the analytical methods. The discard rate of sub-assemblies while

the discard policy is applied could be unacceptable for the practitioner, as mentioned

earlier. Therefore, we have imposed the adaptability of manufacturing process into

selective assembly systems in order to reduce the discard rate.

In this chapter, first we describe our extended analytical performance evaluation method

of selective assembly systems including the new adaptability policy to reduce the dis-

card rate of sub-assemblies. Then, we describe our optimal adaptability design method

which contributes to minimize the surplus sub-assemblies. The effect of proposed pro-

cess adaptability on the system performance of the selective and adaptive assembly

systems with realistic system setting is described later. Finally we compared the re-

sults of the proposed optimal shift design method to that of previous versions.

5.1.1 Process Adaptability Approach To Reduce The Discard Rate:

Analytical Approach

The discard policy which is applied in the performance evaluation of selective assem-

bly systems caused a large number of sub-assemblies to be neglected. The discard is

ruled when the upstream manufacturing machines face one of the buffers full and they

randomly produce the sub-assembly to be placed in the full buffer. In fact, the dis-

carded sub-assembly is a conforming sub-assembly which is neglected due to the logistic

84


complexity of the system. Therefore, we have proposed a method to reduce the the

discard rate. In the literature, the process adaptability is imposed to the process mean

with the determined probability. While we proposed to adjust the process mean of the

manufacturing process with smaller variation only when one of the buffers of the

machine is full. In the other words, the process is adapted to another process mean

only when it is needed based on the buffer levels.

In order to extend our analytical performance evaluation model, we need to include

the process adjustment for the manufacturing machine of the more capable process.

We have considered the My machine to be the more capable manufacturing machine.

Therefore we need to modify the Markov model of the My in machine level decompo-

sition algorithm. In the following we describe the required modifications.

5.1.1.1 Sub-assembly Manufacturing Machine My

We assume the process adjustment requires negligible set-up times (only process target

adjustments). A shift τ modifies the process mean level µy(τ) = µy + δ(τ). Therefore,

it affects the sorting probabilities of the component y in the downstream buffers as

follows:

αy(τ)i =

∫ Lxi

lxi

Fx(τ)(s)ds ∀i = 1, .., F (5.1)

where Fy(τ) is the cumulative probability function of the shifted distributions with

mean µy(τ) and standard deviation σy. The fraction of components y produced under

the target process mean µy(τ) is denoted as ϑi(τ). Since it involves a change in the

quality feature distribution of one component, the process adaptation modifies the as-

sembly yield. Under process shift τ , the adjusted fraction of non-conforming assembled

products for flow i is γai (τ) which obviously differs from the non-adjusted process mean.

State Transition Diagram. Depending on the level of the adjacent buffers, ma-

chine My behaves as reported in Table 5.1. As it can be noticed, the discard policy

affects the behavior of the machine in the states where one of the two buffer is full and

the other is not full (row 1 to row 4). In these conditions, process adjustment can be

85


Buffers Part qualityMachine State

Discard Rule

Bx1 By

2 Class Output

Buffer

Prob.

Not Full Full 1 UP(W 1B2) By1 α

y(τ)1

Not Full Full 2 UP(W 1B2) discard αy(τ)2

Full Not Full 1 UP(B1W 2) discard αy(τ)1

Full Not Full 2 UP(B1W 2) By2 α

x(τ)2

Not Full Not Full 1 UP(W 1W 2) By1 αy1

Not Full Not Full 2 UP(W 1W 2) By2 αy2

Full Full 1-2 BL(B1B2) / /

Not Full Full 1-2 DOWN(RB2) / /

Full Not Full 1-2 DOWN(B1R) / /

Not Full Not Full 1-2 DOWN(R) / /

Table 5.1: Behavior of machine My. ”B” denotes blocking states, ”W” denotes opera-


activated and the sorting probabilities are dependent on the shift entity δk, as expressed

in equation (5.1). The Markov chain representing the behavior of the component man-

ufacturing machine My is represented in Figure 5.2 (to simplify the picture, transition

probability p̄ is shown instead of 1 − p; moreover P1 =∑Ty

t=1 pyt +

∑Ta+1+Txk py,b,1k ).

The probability of failure and repair of machine My, i.e. py and ry, are known since

they are input data of the problem. The probabilities of transition to blocking states

are unknown but have been derived in the BLD similar to the non-adjustable model

presented in “Selective Assembly System Conventions, System Description and Ana-

lytical Performance Evaluation Methodology” chapter. Therefore, all the transition

probabilities in this Markov chain are known.


state probabilities of Markov chain characterizing the My behavior can be derived.

Then, its behavior is approximated by simplified multiple failure machine models of

the upstream pseudo-machines Mu,y(i), i = 1, 2. The Markov chain in Figure 5.2 can

be solved and the steady-state probabilities can be calculated. Then, the Markov model

representing the My behavior is transformed into the Markov chain represented in Fig-

86


Figure 5.2: Markov model characterizing the Machine Y, My, with process adjustments.

87


Figure 5.3: Pseudo machine state transition diagram.

ure 5.3 which is similar to that of manufacturing machine with no process adjustment.

The transformation is made through the re-distribution of the calculated steady-state

probabilities, performed by using the following State Aggregation Equations: For ex-

ample, for Mu,y(1), the following equations are adopted (π(· · · ) is representing the

steady-state probability of the state in brackets):

π (W u,y(1)) = π(W 1W 2

)αy1 + π

(W 1B2

)αy(τ)1 (5.2)

π(W̄ u,y(1)

)= π

(W 1W 2

)αy2 + π

(W 1B2

)αy(τ)2 (5.3)

π (Bu,y(1)) = π(B1W 2

)+ π

(B1B2

)+ π(B1R2) (5.4)

π (Ru,y(1)) = π(R1B2

)+ π (R) (5.5)

Similar equations apply to Mu,y(2). From the point of view of the material flow

entering buffer By1 , the throughput of scrapped of parts due to the discard policy

(π(W 1B2

)αy(τ)2 ) can be seen as an interruption of flow due to the competition failure

state W̄ u,y(1). Moreover, the fraction ϑi(τ) of parts produced under the target process

mean µy(τ) can be computed as:

ϑ1(τ) =π(W 1B2)α

x(τ)1

π(W u,x(1))ϑ2(τ) =

π(B1W 2)αx(τ)2

π(W u,x(2))(5.6)

88


Inputs to the BLD. With similar approach we need to transfer the machine failures

to the upstream Pseudo machines which represent the My. The probability of Mu,y(i)

failing in local mode can be obtained as:

pu,yt (1) =π (Ru,yt (1))

π (W u,y(1))ru,yt (1) t = 1, .., Ty (5.7)

The probabilities of failure and repair for the competition failure mode can be derived

as follows:

pu,yTx+1(1) =π(W̄ u,y(1)

)π (W u,y(1))

ru,yTy+1(1) (5.8)

ru,yTy+1(1) = αy1(1−Ty∑t=1

pyt )

5.1.1.2 The Effect of Process Adaptation On the System Performance

The system parameters is presented in Table 5.2. .The buffer sizes are all set to 3 and

this is because the machines reliability are the same and the equal buffer size is the

best approach for buffer allocation in this particular system configuration . If By1 is

full, the target mean of the more capable process My is shifted to µy(τ) = µy + δ.

Results are reported in Figure 5.4. As it can be noticed, the shift has a double effect

on the performance of the system. On the one hand, it increases the total production

rate of the system, by decreasing the probability of producing a quality class i part

when buffer Byi is full. On the other hand, by increasing the shift, the yield increases

up to a certain level, and then it decreases. As a result of this competing effects, the

effective production rate is a concave function that is maximized for a certain value

of the shift entity δ = 0.07. For this level, the effective throughput of the system is

consistently higher than the effective throughput without process adaptation (δ = 0).

It is worth to mention that, in the proposed case, the yield is maximized for δ = 0.056.

This means that a methodology that neglects the interactions between quality and

production logistics, only provides sub-performing configurations of the system.

5.1.2 The Optimal Process Shift Design in Selective and Adaptive

Assembly Systems

In this section we address the problem of optimally selecting the number of shifts of pro-

cess mean in selective and adaptive assembly systems. Moreover, we will demonstrate

89


Mx My Ma


2y) Z = X −Y ; Z ∼ N(µx−µy, σ

2x +σ2

y)

µx=4; σx=0.116 µy=3.3; σy=0.05 µz=0.7; σz=0.126


αx1=0.5 αx

2=0.5 αy1=0.5 αy

2=0.5 αa1 , αa

2 : 0.5

γx ≈ 0 γy ≈ 0

γ ≈ 0.4761 if F = 1,

γ1 = γ2 ≈ 0.2881 if F = 2

px = 0, 01, rx = 0, 05 py = 0, 01; ry = 0, 05 pa = 0, 01, ra = 0, 05

Table 5.2: Summary of the adopted parameters.

Figure 5.4: Effect of Shifts on System performance.

90


the effect of the proposed optimal design on the throughput and logistics performance

of the system, showing great benefits towards state-of-the-art approaches.

5.1.2.1 Modeling Assumptions

Sub-assembly key characteristics distribution. We assume the assembly of two

sub-assemblies, namely X and Y. The key quality characteristic of sub-assembly X,

named x, is assumed to be normally distributed, i.e. N(µx, σx). The key quality char-

acteristic of sub-assembly Y, namely y, is assumed to be normally distributed with

mean µy and variance σ2y = (τσx)2, where τ is the ratio between the standard devia-

tion of Y and X, 0 ≤ τ ≤ 1. The clearance between the two components is C with

tolerance ∆ (the acceptable clearance range is within C ±∆). The process mean shift

(the magnitude of the process adjustment) is assumed to be applicable only to the low-

est variance component Y. Each shift is defined by a process mean shift magnitude of bi

from the nominal process mean µy and an associated shift probability of pi. Symmet-

ric process mean shifts to right and left are assumed, i.e. each shift with magnitude bi

has a corresponding shift with magnitude −bi, both having probability pi of occurrence.

The total number of process target values is denoted with S and the corresponding

shift levels and probabilities are the element of the vectors b and p. In this settings,

S = 1 means that there is unique process target value, i.e. no shift is implemented.

The overall component distribution is built as the probability-weighted sum of shifted

distributions. Figure 5.5 shows a distribution for a five-shift design.

The fraction of components X and Y that is out of specification limits is denoted

respectively as γx and γy. These fractions can be calculated as:

γx = probability{x<LSLx ∪ x>USLx} (5.9)

γy = probability{y<LSLy ∪ y>USLy}

where the LSL and the USL are respectively the lower and the upper specification

limits imposed on the sub-assemblies by design. We assume that out of specification

sub-assemblies are scrapped by the measurement stations prior to the classifications.

91


Figure 5.5: Five symmetric shifts of process mean for Y.

Partitioning Scheme. Sub-assemblies are partitioned according to the equal-width

partitioning scheme. The width of each partition is w = 2D/n, where 2D=USL-LSL.

The number of bins n can be chosen to have 0 ≤ w ≤ ∆, i.e. all the coupled sub-

assemblies are within the acceptable clearance range thus being conforming assembled

parts. In this model, design specification widths are assumed to be equal for both

components, Dx = Dy = D. Clustering bins are built as follows:

(x0, x1, ..., xn−1, xn) = (µx −D,µx −D + w, ..., µx +D − w, µx +D) (5.10)

(y0, y1, ..., yn−1, yn) = (µy −D,µy −D + w, ..., µy +D − w, µy +D)

where, (xi−1, xi] and (yi−1, yi] are the boundaries of each partition i = 1, .., n for com-

ponent X and component Y, respectively.

Performance Measures. The performance measures of interest for optimal shifts

design are considered as follows:

• R(S, b, p) is the matching probability, i.e. the probability of matching compo-

nents X and Y of corresponding buffers, under S process mean levels and shift

parameters b and p.

92


• TH is the average throughput of the system, i.e. the number of parts produced

in a time unit. In this model the THTot = THEff = TH. This is because

the number of quality classes are considered so that all the assembled parts are

conforming after assembly process.

• WIP is the average level of work-in-progress, i.e. the total number of components

X and Y waiting in bins for assembly.

5.1.2.2 Matching Probability Evaluation Method

To evaluate the matching probability R(S, b, p), we set Ri(S, b, p) as the probability of

matching sub-assembly X and Y for partition i, where i = 1, .., n. The probability PX,i

of releasing a component X in partition i is:

PX,i = FX(Xi)− FX(Xi−1) (5.11)

FX = Φ ((X − µx)/σx)

Where Φ(x) is the standard cumulative normal distribution. Similarly, the probability

of releasing component Y in partition i, PY,i, is:

PY,i = FY (Yi)− FY (Yi−1) (5.12)

In case S shifts are implemented to the target mean of sub-assembly Y, the cumulative

distribution function of Y is:

FY (y) =(1− 2

(S−1)/2∑i=1

Pi)Φ((y − µy)/σy)+ (5.13)

(S−1)/2∑i=1

Pi [Φ(y − µy − bi)/σy + Φ((y − µy + bi)/σy)]

Therefore, the matching probability of each partition is:

Ri(S, b̄, p̄) = Min{FX(Xi)− FX(Xi−1), FY (Yi)− FY (Yi−1)} (5.14)

and the total matching probability is:

93


R(S, b̄, p̄) =

n∑i=1

Ri(S, b̄, p̄) (5.15)

It is worth to mention that there exists a limit value of this matching probability, called

Rlim, which is related to the fraction of scrapped components as follows:

Rlim = min {1− γx, 1− γy} (5.16)

The corresponding number of shifts is Slim. It is remarkable to notice that increasing

the number of shifts beyond Slim does not provide any additional contribution to the

matching probability increase.

5.1.2.3 Shift Design Optimization

Formulation of optimization problems. In order to derive the optimal shift design

of selective and adaptive assembly systems, two optimization problems are formulated

and solved.

Problem 1: Maximization of the matching probability

The objective is to find the maximum matching probability R(S, b, p), for a given value

of S. The decision variables are b and p for the corresponding value of S. The following

constraint optimization problem is solved:

max.x

R(S, b, p)

s.t. pi ≥ 0 ∀i = 1, ..., (S − 1)/2

1− 2

(S−1)/2∑i=1

Pi ≥ 0

b1 ≤ b2 ≤ ... ≤ b(S−1)/2

(5.17)

The first and second constraints impose that the probabilities of each shift must be

non-negative. The third constraint imposes that each shift magnitude must be larger

than the previous one.

94


Figure 5.6: Block Diagram for Problme 2.

Problem 2: Optimal number of shifts

The objective is to find the optimal number of shifts S* which corresponds to a required

target matching probability R*(S,b,p). The formulation of problem 2 is:

min.s

S

s.t. R(S, b̄, p̄) ≥ R∗(S, b̄, p̄)(5.18)

Solution of the Optimization Problem. The method used to solve problem 1 is

inspired by Matsuura and Shinozaki [2011b] and is based on non-linear optimization.

While approaching problem 2, we first check the existence of a feasible solution to

the problem. The required matching probability R∗ should be lower than the overall

maximum matching probability Rlim. If this condition holds, the solution of Problem

2 is found by applying the algorithm described in Figure 5.6. If the required match-

ing probability R∗ is attained with no shift (S = 1) of process Y, there is no need to

adapt the process. Otherwise, we increase the number of shifts (S = S + 2) and we

solve Problem 1 to find the maximal attainable matching probability with the updated

number of shifts. This procedure is repeated until the target matching probability is

met. The corresponding shift value solves Problem 2.

95


Upon convergence, the vectors b and p contain the optimal design of the process shift

levels and the associated probabilities.

Numerical Results. In the following, two numerical examples that show the benefits

of the proposed approach with respect to state of the art process shift design methods

are extensively reported. In both the cases the required matching probability, R∗, is

set to 99%. The sample case data are reported in Table 5.3.

ParametersExperiments

1 2

µx 4 2.75

σx 0.116 0.15

µy 3.3 2.5

σy 0.05 0.045

D 0.35 0.45

n 8 10

D ±∆ 0.7± 0.09 0.25± 0.09

Table 5.3: Sample case data.

Case 1. Based on the reject fractions of components X and Y, the overall maximum

matching probability Rlim is 99.73%, which is higher than required matching probabil-

ity. Applying the procedure explained in the previous section solves Problem 2. Table

5.4 shows the maximum matching probability for increasing process adaptation levels.

As it can be observed, for 5 target levels, the maximum matching probability of 99.7%

meets the required matching probability of 99%, demonstrating that with our method

it is possible to achieve the required matching probability R∗.

If compared to the existing methods to support 3-shift process design developed in Mat-

suura and Shinozaki [2011b] and Kannan and Jayabalan [2002], the proposed method

shows marked improvement in terms of matching probability. There is a 1.7% improve-

ment of matching probability of the proposed optimal 5-shift design towards the 3-shifts

design proposed by Matsuura and Shinozaki [2011b] and 8.5% improvement compared

to the 3-shift design of Kannan and Jayabalan [2002]. It is worth highlighting that

96


Iteration Shift Matching Probability

1 1 62.68%

2 3 98%

3 5 99.73%

4 7 99.73%

5 9 99.73%

Table 5.4: Maximum matching probability for a given number of shifts in Case 1.

Figure 5.7: Matching probability as a function of the number of shifts - Case 1.

the methods proposed in Matsuura and Shinozaki [2011b] and Kannan and Jayabalan

[2002] do not allow to meet the matching probability requirement. Figure 5.7 graphi-

cally depicts the improvements of our method compared to these previous designs.

Table 5.5 illustrates the details of the partitioning design and the corresponding match-

ing probabilities when the process is not adapted, i.e. no shift is applied. As it can be

noticed, by adapting the process target values according to the optimal process shift

design proposed in this paper an increase of the matching probability of about 60%

in the matching probability is met towards the case where no adaptation is applied.

This practically means a consistent reduction of the work in progress and a consistent

97


increase in the system throughput. Table 5.6 illustrates the specific results of the meth-

ods proposed by Matsuura and Shinozaki [2011b] and Kannan and Jayabalan [2002]

and the proposed optimal shift design.

Bin number

Partitioning Probabilities

X YX Y Ri

Min Max Min Max

3.65 2.95 0.00 0.00

1 3.65 3.74 2.95 3.04 0.01 0.00 0.00

2 3.74 3.83 3.04 3.13 0.05 0.00 0.00

3 3.83 3.91 3.13 3.21 0.16 0.04 0.04

4 3.91 4.00 3.21 3.30 0.27 0.46 0.27

5 4.00 4.09 3.30 3.39 0.27 0.46 0.27

6 4.09 4.18 3.39 3.48 0.16 0.04 0.04

7 4.18 4.26 3.48 3.56 0.05 0.00 0.00

8 4.26 4.35 3.56 3.65 0.01 0.00 0.00

4.35 3.65 0.00 0.00

Matching 0.627

Surplus 0.371

Table 5.5: Binning and probabilities for Case 1, without process adaptation.

Case 2. Experiment 2 differs from experiment 1 since the capability of the process that

produces component Y is higher. The results for Case 2 are given in Table 5.7. Again,

a five-shift design results to be optimal in these settings. As it can be seen from Table

5.7, there is 5.7% improvement in terms of matching probability between the 3-shifts

design proposed by Matsuura and Shinozaki [2011b] and our optimal 5-shifts design.

The matching probability improvement of our optimal design compared to the 3-shifts

design proposed by Kannan and Jayabalan [2002] is about 19%. Figure 5.8 shows the

impact of increasing shift on the matching probability for Case 2. Table 5.8 illustrates

the details of the partitioning design and the corresponding matching probabilities

when the process is not adapted. Again, it can be noticed that by adapting the process

target values following the proposed optimal process shift design an increase of the

matching probability of about 95% is met, towards the case where no adaptation is

98


3-shifts [Kannan and

Jayabalan [2002]]

(b∗, p∗ )=(0.139,0.286)

3-shifts [Matsuura and

Shinozaki [2011b]]

(b∗, p∗ )=(0.171,0.35)

5-shifts proposed

optimal design

(b∗1, b∗2, p

∗1, p

∗1 )=

(0.133,0.262,

0.225,0.022)

Bin n◦ X Y Ri X Y Ri X Y Ri

0.001 0.000 0.001 0.000 0.001 0.001

1 0.011 0.002 0.002 0.011 0.002 0.0023 0.011 0.011 0.011

2 0.055 0.066 0.055 0.055 0.063 0.0546 0.055 0.055 0.055

3 0.160 0.192 0.160 0.160 0.160 0.1598 0.160 0.160 0.160

4 0.273 0.240 0.240 0.273 0.274 0.2734 0.273 0.273 0.273

5 0.273 0.240 0.240 0.273 0.274 0.2734 0.273 0.273 0.273

6 0.160 0.192 0.160 0.160 0.160 0.1598 0.160 0.160 0.160

7 0.055 0.066 0.055 0.055 0.063 0.0546 0.055 0.055 0.055

8 0.011 0.002 0.002 0.011 0.002 0.0023 0.011 0.011 0.011

0.001 0.000 0.001 0.000 0.001 0.001

Matching 0.912 0.980 0.997

Surplus 0.085 0.017 0.003

Table 5.6: Details results in the application of three alternative methods for Case 1.

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Figure 5.8: Matching probability as a function of the number of shifts - Case 2.

applied. Therefore, the benefits of the proposed approach increase when the process

that is shifted is more capable. Table 5.9 illustrates the specific results of the methods

proposed by Matsuura and Shinozaki [2011b], Kannan and Jayabalan [2002] and the

optimal shift design proposed, for Case 2.

Iteration Shift Matching Probability

1 1 49.68%

2 3 93.57%

3 5 99.33%

4 7 99.73%

5 9 99.73%

Table 5.7: Maximum matching probability for a given number of shifts in Case 2.

5.1.3 The Effect of Optimal Process Adaptation on the System Per-

formance Applying Simulation Model

In order to analyze the impact of the developed process adaptation design method on

the integrated quality and logistics performance of the overall selective and adaptive

assembly systems a discrete event simulation model was developed. This simulation

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Bin number

Partitioning Probabilities

X YX Y Ri

Min Max Min Max

2.30 2.05 0.0014 0 0

1 2.30 2.39 2.05 2.14 0.0068 0.000 0.000

2 2.39 2.48 2.14 2.23 0.027 0.000 0.000

3 2.48 2.57 2.23 2.32 0.079 0.000 0.000

4 2.57 2.66 2.32 2.41 0.1598 0.02 0.02

5 2.66 2.75 2.41 2.50 0.2257 0.48 0.23

6 2.75 2.84 2.50 2.59 0.2257 0.48 0.23

7 2.84 2.93 2.59 2.68 0.1591 0.02 0.02

8 2.93 3.02 2.68 2.77 0.0790 0.000 0.000

9 3.02 3.11 2.77 2.86 0.0277 0.000 0.000

10 3.11 3.20 2.86 2.95 0.0068 0.000 0.000

3.20 2.95 0.0014 0.000 0.000

Matching 0.5

Surplus 0.5

Table 5.8: Binning and probabilities for Case 2, without process adaptation.

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3-shifts [Kannan and

Jayabalan [2002]]

(b∗, p∗ )=(0.171,0.35)

3-shifts [Matsuura and

Shinozaki [2011b]]

(b∗, p∗)=(0.17,0.27)

5-shifts proposed

optimal design

(b∗1, b∗2, p

∗1, p

∗1 )=

(0.156,0.304,

0.2365,0.044 )

Bin n◦ X Y Ri X Y Ri X Y Ri

0.001 0.000 0.001 0.000 0.001 0.000

1 0.007 0.000 0.000 0.007 0.000 0.000 0.007 0.005 0.005

2 0.027 0.004 0.005 0.027 0.004 0.004 0.027 0.031 0.028

3 0.079 0.142 0.079 0.079 0.111 0.079 0.079 0.078 0.079

4 0.160 0.196 0.159 0.160 0.159 0.159 0.160 0.159 0.159

5 0.226 0.156 0.156 0.226 0.226 0.226 0.226 0.226 0.226

6 0.226 0.156 0.156 0.226 0.226 0.226 0.226 0.226 0.226

7 0.159 0.196 0.159 0.159 0.159 0.159 0.159 0.159 0.159

8 0.079 0.142 0.079 0.079 0.111 0.079 0.079 0.078 0.079

9 0.028 0.004 0.005 0.028 0.004 0.004 0.028 0.031 0.028

10 0.007 0.000 0.000 0.007 0.000 0.000 0.007 0.005 0.005

0.001 0.000 0.001 0.000 0.001 0.000

Matching 0.798 0.936 0.993

Surplus 0.202 0.064 0.007

Table 5.9: Details results in the application of three alternative methods for Case 2.

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Figure 5.9: Schematic representation of selective and adaptive assembly systems for the

experiments.

model includes realistic assumptions on the overall system behavior that are summa-

rized in the next section.

Simulation Model Assumptions. Selective and adaptive assembly systems where

sub-assemblies X and Y are assembled are considered. The system layout is repre-

sented in Figure 5.9, where machining and assembly stations are represented as light

blue squares, inspection stations are represented as red squares and buffers are repre-

sented as yellow circles.

The components X and Y are respectively processed by machines Mx and My. They

are considered to be unreliable and subject to failures. For machine Mx (My) the prob-

ability of failure is px = 1/MTTFx(py = 1/MTTFy) and the probability of repair is

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rx = 1/MTTRx(ry = 1/MTTRy). It is assumed that there is always available material

upstream Mx and My, i.e. they are never starved.

After the process, each component is inspected and sorted into the downstream bins

according to the measured dimensional key characteristic. In line with the previously

introduced assumptions, a total number of n quality classes are defined for both X and

Y, namely Bxi and By

i , with i = 1, ., n. The capacity of each buffer is finite and equal

to Nxi and Ny

i , which are natural numbers.

The assembly station MA, takes one sub-assembly X and one of sub-assembly Y from

the corresponding bins and assemble them. Matching process is assumed as one by

one matching between buffers of sub-assembly X and Y. In other words, the assembly

machine Ma can assemble sub-assemblies X in buffer Bxi only with sub-assemblies Y in

Byi , with i = 1, , n. The assembly station is also assumed to be unreliable and subject

to failures. In details, MA fails with probability Pa = 1/MTTFa and is repaired with

probability ra = 1/MTTRa.

The material flow dynamics is modeled by a discrete flow of parts. Each machine has

the same processing time, scaled to the time unit. If operational, a machine starts

processing one part at the beginning of the time unit. The buffer levels are updated

at the end of the time unit. Inspection stations are assumed to take negligible time to

measure the components.

In order to avoid the deadlock state, in this model we select the discard policy. Accord-

ing to the discard policy , whenever a sub-assembly is produced, either at machine Mx

or My and the buffer where it should be placed is full, the component is discarded. As

mentioned earlier, although this strategy entails a loss of system total throughput, it

allows avoiding deadlock states.

Simulation Results. The optimal shifts designs obtained for the two previously

analyzed experiments have been tested at system level with the simulation model.

In addition to the data reported in Table 5.3, failure probabilities have been set to

px = 0.034, rx = 0.43, py = 0.034, ry = 0.43, pa = 0.033, ra = 0.33. As a consequence,

104


the assembly station results to be the bottleneck machine in the system, with an iso-

lated efficiency of 0.9 (both Mx and My have efficiency equal to 0.924). All buffer sizes

are set to 40. The experiments were run for 20 replicates of approximately 18,000 time

units of operation. Table 5.10 shows the simulation results for Case 1. 95% confidence

interval widths are 0.01% and 4% of the average throughput and the WIP, respectively.

Shift ETot. WIP

1 0.58 305.11

3∗ 0.84 269.26

3 0.89 203.97

5 0.90 127.71

Table 5.10: Case 1: Simulated total throughput and WIP for different shifts designs (3*

denotes the 3-shifts design proposed by Kannan and Jayabalan [2002]).

For Case 1, the proposed optimal 5-shifts design improved the total throughput of the

system by 53%, 6%, and 1% compared to no-shift design, 3-shifts design proposed by

Kannan and Jayabalan [2002], and 3-shifts design proposed by Matsuura and Shinozaki

[2011b], respectively. It also significantly reduced WIP, by approximately 58%, 53%,

and 37% comparing to no-shift design, 3-shifts proposed by Kannan and Jayabalan

[2002] and 3-shifts proposed by Matsuura and Shinozaki [2011b], respectively. Figure

5.13 and 5.11 show the observed throughput and WIP.

Table 5.11 shows the simulation results for throughput and WIP applying different

shifts designs for Case 2. The optimal 5-shifts design improved throughput of the sys-

tem by 92%, 20%, and 5.9% compared to no-shift design, the 3-shifts design proposed

by Kannan and Jayabalan [2002], and the 3-shifts design proposed by Matsuura and

Shinozaki [2011b]. The WIP is reduced by 47%, 43% and 34% compared to no-shift

design, to the 3-shifts design proposed by Kannan and Jayabalan [2002], and to the

3-shifts design proposed by Matsuura and Shinozaki [2011b]. Figure 5.13 and 5.13 show

the optimal design improvements on system throughput and WIP, respectively.

As shown by this set of results, by adapting the process target with the proposed ap-

proach the throughput of the system can be improved by simultaneously reducing the

105


Figure 5.10: Observed throughput under different shifts designs for case 1.

Figure 5.11: Observed WIP under different shifts designs for case 1.

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Figure 5.12: Observed throughput under different shifts designs for case 2.

Figure 5.13: Observed WIP under different shifts designs for case 2.

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Shift ETot. WIP

1 0.4638 378.4

3∗ 0.7399 355.4

3 0.8427 305.8

5 0.8928 200.7

Table 5.11: Case 2: Simulated total throughput and WIP for different shifts designs (3*

denotes the 3-shifts design proposed by Kannan and Jayabalan [2002]).

work in progress of the system and meeting high product quality standards. The results

of this analysis is published in Colledani and Ebrahimi [2012].

In particular, we showed that the proposed method to derive the optimal number of

process shifts outperforms existing techniques. Results show that process adaptation

may help to increase the matching probability in the system and, consequently, to

increase the system production rate and to decrease the system WIP, while meeting

desired product quality targets.

In this chapter we have analyzed and explore the behavior of the selective and adaptive

assembly systems. In particular, we have applied the process adaptation in the manu-

facturing process in order to reduce the discard rate of sub-assemblies. The proposed

method is modeled within the analytical performance measurement framework of the

selective assembly systems which is addressed in previous chapters. Moreover, the pro-

posed optimal process adaptation design is addressed. Finally, we illustrate the effect

of process adaptation in system level performance of selective and adaptive assembly

systems. We have shown that the optimal process adaptation design can considerably

reduces the WIP while increases the throughput of the system. Although the process

adaptations are significantly beneficial to increase the efficiency of the selective assem-

bly systems, but not all the manufacturing processes are able to produce with several

mean target values. Therefore, we proposed new intelligent flow control policies to

handle better the logistic complexity of the selective assembly systems. In the next

chapter we explore the proposed policies and their effect on the deadlock state and the

consequent discard rate.

108

6

Deadlock State Correction

Policies

In order to manage the deadlock states, we proposed 5 new flow control policies. These

innovative policies are based on the observable state of the system. The proposed

policies are embedded within our simulation model and the effects of each policy on

system level performance is explored analyzed. There are two different type of policies:

Assembly level policies and Sub-assembly manufacturing level policies. In the following

section we describe the policies in details and then we will discuss about the selective

assembly system behavior under the proposed policies in the next section.

6.1 Assembly Level Policies

Reactive Class Mixing. When the selective assembly system is in deadlock state,

the assembly machine is starved because there are no coupled non-empty buffers to

select for assembly operation. At the same time, both sub-assembly manufacturing

machines are blocked due to a single full buffer. In reactive class mixing of assembly

level policies, we proposed to rule the assembly machine to mix the sub-assemblies

of uncoupled buffers which are non-empty. In the other words, when the assembly

machine is starved while there are unmatched sub-assemblies, the assembly machine

selects the available sub-assemblies although they do not belong to the same quality

class. Figure 6.1 depicts graphically this policy. The black circles depicts the full buffer

while the white circle shows the empty buffer.

109

6. DEADLOCK STATE CORRECTION POLICIES

Figure 6.1: Assembly Level Policies: Reactive Class Mix.

It must be notice that, the manufacturing machines are blocked when only one buffer

is full following the blocking before service assumption. Thus the system generates no

discarded sub-assemblies. In fact, the benefit of zero discard rate is paid by the cost

of mixed class assemblies and the consequent decreased system yield level. These kind

of assemblies (the mixed quality class), still can be conforming however it depends on

the partitioning policy and the key characteristic distribution of sub-assemblies.

Preventive Class Mixing. As it can be realized from the name of this policy, the

assembly machine prevents the deadlock state through mixing the unmatched quality

classes prior to the deadlock state. This is because the deadlock state is reached from

the particular states in which the assembly machine is starved. This is the reason that

we minimize the starvation probability of assembly machine in this policy. In order

to do so, the assembly machine is permitted to mix the uncoupled classes whenever

it is starved, regardless of the manufacturing machine states. The manufacturing ma-

chines are blocked when only a single buffer is full, therefore there is no discarded

sub-assemblies. This policy is depicted in Figure 6.2 where the gray circles shows non-

empty and not full buffers.

110

6.1. ASSEMBLY LEVEL POLICIES

Figure 6.2: Assembly level policies: Preventive Class Mix.

Similar to the Reactive Class Mixing policy, the benefit of zero discard sub-assemblies

are paid by the mixing of the quality classes. The main difference to the Reactive Class

Mixing is the fact that in Preventive Class Mixing, the assembly machine mixes the

quality classes much more frequent. This is because the assembly machines mixes the

quality classes whenever it is starved and does not wait for the deadlock state to occur.

The system yield is expected to be reduced comparing to the Reactive Class Mixing,

while the total throughput is expected to be increased.

Buffer Level Dependent. In general, the final assembled product in selective as-

sembly system have the same essence. This means there are no specific preference

within the assembled part of first quality classes or the second quality classes. There-

fore, in this policy the assembly machine is permitted to select the coupled buffers in

such a way that the blocking probability for the manufacturing machines are reduced,

following the algorithm represented in 1.

It must be notice that the manufacturing machines follow the discard rule (as shown

in figure 6.3)because the Buffer Level Dependent policy cannot be applied to avoid the

deadlock state. This policy is proposed to reduce the discard rate. Applying this policy

results in the same system yield as the discard rule because the quality classes are not

mixed by the assembly machine. Meanwhile, the discard rate is expected to be reduced

because the assembly machine reacts smart to the system state in terms of buffer levels.

The assembly machine selects the coupled buffers that is more probable to be full. In

111


Algorithm 1: Buffer Level Dependent

if Max{BX1levelBX1Size

, BY1levelBY1Size

}>Max

{BX2level/BX2SizeBY2level/BY2Size

}then

Select the x1 and y1 matches;

else if Max{BX1levelBX1Size

, BY1levelBY1Size

}<Max

{BX2level/BX2SizeBY2level/BY2Size

}then

Select the x2 and y2 matches;

else

go to αa strategy;

end

Figure 6.3: Assembly Level Policy: Buffer Level Dependent.

this way it reduces the probability of blocking of the manufacturing machines. This

leads to reduced discard rate.

6.2 Sub-assembly Manufacturing Level Policies

The second type of the deadlock correction policies are concern with the sub-assemblies

manufacturing level. In these set of policies, the assembly machine remains with the

same policy as the original selective assembly system, it means the selection of the

sub-assemblies is based on matching sub-assemblies from the coupled buffers . Thus,

these set of policies are imposed only on the manufacturing machines. The proposed

policies are introduced to improve the system level performance of selective assembly

systems in terms of the discard rate reduction.

112

6.2. SUB-ASSEMBLY MANUFACTURING LEVEL POLICIES

Figure 6.4: Manufacturing machine level policies: System Level Discard.

System Level Discard Policy. By following the traditional discard policy the sys-

tem state is neglected when the sub-assemblies are discarded. In the other words, the

discard policy is imposed to the manufacturing machines regardless of the system state.

The traditional discard policy permits the manufacturing machines to process a sub-

assembly whenever there is a full buffer downstream. If the processed sub-assembly

has to be placed in the full buffer the machine discards it. In fact, the manufacturing

machines discard the sub-assemblies in states which are not deadlock state in addition

to the deadlock states. For example, considering the selective assembly system with two

classes, if the assembly machine is not starved, thus the system is not in deadlock state,

and one of the buffers of manufacturing machines is full, the manufacturing machine

might discard the sub-assemblies due to the discard policy. However in our proposed

policy, System Level Discard Policy, the manufacturing machines are allowed to follow

the discard rule only if the system is in deadlock state. In the other words, the discard

policy is applied by considering the system state and not only the manufacturing ma-

chines’ state. The schematic view of the system level discard policy is shown in Figure

6.4. Again, the black circles indicate the full buffers and the white circles represent the

empty buffer.

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Figure 6.5: Manufacturing machine level policies : System Level Discard 1 Machine.

System Level Discard Policy Single Machine. In some assemblies one of the

sub-assemblies is much more expensive comparing to the other one. Therefore, it

is not economical to discard both of them even with the proposed reduced discard

rate. Therefore, we proposed to impose the system level discard rule for only the

manufacturing machine that processes the cheaper sub-assembly. In the other words,

the selective assembly system continue the production until it goes to deadlock state

and then only one of the manufacturing machines follow the discard rule. Figure 6.5

represents the System Level Discard Policy Single Machine.

6.3 Numerical results of the deadlock correction policies

As mentioned before, the proposed policies are implemented in the simulation mod-

els. We have tested the proposed policies for 6 different set of experiments to observe

the system level performance measures. In these experiments we have assumed the

assembly of two sub-assemblies, namely X and Y. Sub-assemblies key characteristics

are distributed normally. Each sub-assembly is classified in two quality classes. The

final assembled product key characteristics is identified as the clearance between two

sub-assemblies, namely X−Y . The machines are unreliable and buffer sizes are limited

(fixed to 10 for each buffer).

114

6.3. NUMERICAL RESULTS OF THE DEADLOCK CORRECTIONPOLICIES

Due to the fact that the proposed policies effects depend on the sub-assemblies key

characteristic distribution and the final assembly tolerance limits, we have design the

experiments by considering the machine and buffer parameters as fixed numbers. The

parameters that we have considered as variables are σx, the process variation of the

sub-assembly X and τ as the tolerance of the clearance between the two sub-assemblies

key characteristics (X − Y ). For σx we considered two levels while for the clearance

tolerance we have considered three levels. Levels of σx are considered as 0.06 and 0.12,

that is σx/σy = 1.2 and σx/σy = 2.4, respectively.

6.3.1 Experiments

Table 6.1 shows the considered parameters of all the experiments. For each experiment

we run the simulation model for 10 replications of 900000 time unit, 100000 time unit

is considered for warm-up period. The detail results of each experiment including the

confidence intervals are provided in Tables 6.2, 6.3, 6.4, 6.5, 6.6 and 6.7.

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Experimental Plan

X Y Z

X (µx, σ2x) Y (µy, σ

2y) Z (µx − µy, σ2y + σ2x)

1

µx=4 σx=0.06 µy = 3.3 σy=0.05 µz=0.7 σz=0.0781

1 LSLx = 3.82 USLx = 4.18 LSLy = 3.15 USLy = 3.45 LSLz = 0.65 USLz = 0.75

px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05

2

µx=4 σx=0.06 µy=3.3 σy=0.05 µz=0.7 σz=0.0781

LSLx = 3.82 USLx = 4.18 LSLy = 3.15 USLy = 3.45 LSLz = 0.6 USLz = 0.8

px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05

3

µx=4 σx = 0.06 µy=3.3 σy=0.05 µz=0.7 σz=0.0781


px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05

4

µx=4 σx=0.12 µy=3.3 σy=0.05 µz=0.7 σz=0.0781


px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05

5

µx = 4 σx = 0.12 µy=3.3 σy = 0.05 µz=0.7 σz=0.0781


px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05

6

µx = 4 σx = 0.12 µy=3.3 σy = 0.05 µz=0.7 σz=0.0781


px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05

Table 6.1: Experimental plan for deadlock correction policies.

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Policy TH Tot. CI TH Eff CI System Yield CI Discard Rate CI

Reactive Mix 0,62345 0,0031 0,44311 0,00178 0,71076 0,00089728 0 0

Preventive Mix 0,67835 0,00434 0,47133 0,00247 0,69481 0,00093557 0 0

Sys. Level discard 2M 0,59318 0,00506 0,42982 0,00359 0,72462 0,00094771 0,03055 0,00010003

Sys. Level discard 1 M 0,66013 0,00125 0,47852 0,00119 0,72488 0,00065202 0,07835 0,00097728

Process Adaptation 0,68223 0,00258 0,48817 0,0022 0,71555 0,00108 0,10443 0,00053053

B.L. Dependent 0,6799 0,0031 0,49253 0,00196 0,72442 0,00102 0,12427 0,00037229

Discard 0,67547 0,00306 0,48932 0,00191 0,72441 0,00122 0,14252 0,00071429

Table 6.2: Performance measures results for experiment 1.


Reactive Mix 0,62345 0,0031 0,59115 0,00272 0,9482 0,00048582 0 0

Preventive Mix 0,67835 0,00434 0,63601 0,00407 0,93757 0,00026045 0 0




B.L. Dependent 0,6799 0,0031 0,65037 0,00285 0,95657 0,00038136 0,12427 0,003121

Discard 0,67547 0,00306 0,64611 0,0027 0,95653 0,00033372 0,14252 0,004255


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Reactive Mix 0,62345 0,0031 0,62297 0,00309 0,99924 0,000038355 0 0

Preventive Mix 0,67835 0,00434 0,67739 0,00431 0,99857 0,000054014 0 0




B.L. Dependent 0,6799 0,0031 0,67975 0,00309 0,99979 0,000030846 0,12427 0,00312182

Discard 0,67547 0,00306 0,67533 0,00306 0,9998 0,000012932 0,14252 0,00425528



Reactive Mix 0,62345 0,0031 0,29201 0,00153 0,46839 0,0011 0 0

Preventive Mix 0,67835 0,00434 0,30936 0,00245 0,45604 0,00097963 0 0




B.L. Dependent 0,6799 0,0031 0,32491 0,00173 0,47788 0,00113 0,12427 0,00312182

Discard 0,67547 0,00306 0,32272 0,00191 0,47778 0,00112 0,14252 0,00425528


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Reactive Mix 0,62345 0,0031 0,453 0,00204 0,72662 0,00044662 0 0

Preventive Mix 0,67835 0,00434 0,48462 0,00322 0,7144 0,00029744 0 0




B.L. Dependent 0,6799 0,0031 0,50083 0,00225 0,73663 0,00080086 0,12427 0,00312182

Discard 0,67547 0,00306 0,49739 0,0024 0,73637 0,00094956 0,14252 0,00425528



Reactive Mix 0,62345 0,0031 0,58883 0,00288 0,94447 0,00044606 0 0

Preventive Mix 0,67835 0,00434 0,63732 0,0041 0,93949 0,00015416 0 0




B.L. Dependent 0,6799 0,0031 0,64469 0,00296 0,94821 0,00039811 0,12427 0,00312182

Discard 0,67547 0,00306 0,6406 0,00267 0,94838 0,00056311 0,14252 0,00425528


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Figure 6.6, 6.7, 6.8, 6.9, 6.10 and 6.11 graphically illustrate the effect of proposed

policies on the effective throughput for experiment 1 to 6, respectively. Althought in

most cases our proposed process adaptation policy, which is introduced in chapter

“Selective and Adaptive Assembly Systems”, is out-performing our other flow control

policies in terms of the effective throughput, but the main aim to introduce these new

flow control policies was to reduce the discard rate. The effect of proposed flow control

policies on the discard rate of the system is illustrated in Figure 6.6, 6.7, 6.8, 6.9, 6.10

and 6.11 for experiments 1 to 6, respectively.

For instance, consider the experiment number 4; although in Reactive Mix policy and

Preventive Mix policy the effective throughput is reduced by 9.5% and 4.1%, respec-

tively, comparing to the discard policy, the discard rate is reduced to zero from 0.142

parts per time unit. This is because the manufacturing machines are blocked when

one buffer become full, thus they discard no sub-assemblies while the deadlock state is

avoided. For System level discard 2M, System level discard 1M, Process Adaptation

and Buffer Level dependent policies, the discard rate is reduced by 78.56%, 45.0252%,

26.7260% and 12.8052%, respectively.

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Figure 6.6: Experiment1: Effective throughput behavior for proposed deadlock correction policies.

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6.3. NUMERICAL RESULTS OF THE DEADLOCK CORRECTIONPOLICIES

From the discard reduction point of view, considering the Figures of the discard policy

(Figure 6.12, 6.13, 6.14, 6.15, 6.16 and 6.17), we can conclude that the proposed policies

are all out-performing the Discard Policy which is proposed in the literature. As it can

be noticed from the results, the Preventive Class Mixing and Reactive Class Mixing

policies reduce the discard rate to zero. Taking into account the 6 set of experiments

we can prioritize the policies based on the effect on the discard rate, as following:

1. Reactive Mix

2. Preventive Mix

3. System level discard 2M

4. System level discard 1M

5. Process Adaptation

6. Buffer Level dependent

7. Discard

It must be noticed that this prioritization is not valid if the comparison is carried out

based on the effective throughput.

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7

Selective Assembly Application

in Electrical Engine Production:

Bosch Case

7.1 Introduction

Only limited number of case studies have been analyzed in the literature of manufac-

turing system analysis, although the considerable effort devoted to this research field.

Their aim was mainly to provide practical validation of the analytical models, rather

than supporting the company in the challenging issue of constantly increasing the pro-

ductivity of its manufacturing operations. Therefore, there are only few collaboration

projects between industry and academy where the analytical performance evaluation

tools are applied for system performance estimation and improvement.

Colledani et al. [2010] reported the results of a collaboration project between Politec-

nico di Milano (Milano, Italy), Kungliga Tekniska hogskolan (Stockholm, Sweden) and

Scania CV AB (Sodertalje, Sweden) in the area of manufacturing system productivity

improvement. In this project a high increment in throughput and considerable savings

in work-in-progress (WIP) is achieved in the six-cylinder engine-block manufacturing

system. The project also provided company with an integrated and formalized method-

ology for manufacturing system configuration, reconfiguration and continuous improve-

ment. Freiheit et al. [2007] explore the operational cost differences between high-volume

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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE

serial CNC-based manufacturing systems and parallel CNC-based manufacturing sys-

tems. In Alden et al. [2006] approaches and the results achieved by General Motors

Corporation in a long-term project to evaluate and increase the throughput performance

of its production lines is reported. Patchong et al. [2003] addressed the improvement

method of the car body production at PSA Peugeot Citroen, where an iterative three-

step design method was developed to improve the system throughput. The method

includes both analytical and simulation models. The proposed method improved the

throughput with the minimal capital investment and no compromise in terms of quality.

Liberopoulos and P.Tsarouhas [2002] collaborate in a project to determine cost-efficient

methods of speeding up the croissant processing lines of Chipita International Inc., one

of the largest Greek manufacturers of bakery products and snacks. They have shown

that the proper buffer allocation at a specific point of the line led to a reduction in

failure impact and an increase of the system performance efficiency. Almgren [2000]

considered the experience of Volvo Car Corporation. The author examined the pilot

production and the manufacturing process start-up of the Volvo S80 model. The main

aim of this case study was to contribute to the understanding of the way the ramp-up

process was affected by certain types of disturbances. Burman et al. [1998] studied

on the application of analytical methods to design a system for manufacturing ink-

jet printers at Hewlett-Packard Corporation. Great benefits for the company through

assigning of more buffer space in the manufacturing line supported by the use of ap-

proximate analytical techniques is provided. In this chapter we describe the application

and benefits of implementing selective assembly systems in production of the electrical

engines in Bosch company. The results of the proposed approaches are published as

deliverable of EU funded project (MuProD [2013d]), MuProD “Innovative proactive

Quality control system for in-process multi-stage defect reduction”.

7.2 Bosch Electrical Engine manufacturing system descrip-

tion

The manufacturing system of the Bosch plant producing electrical engines for the e-

mobility sector in Hildesheim is considered for this case study. The electrical engines

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7.2. BOSCH ELECTRICAL ENGINE MANUFACTURING SYSTEMDESCRIPTION

Figure 7.1: Integrated Mototr Generator (Bosch).

are Integrated Motor Generator (IMG), permanent magnet excited synchronous ma-

chine with an inner rotor, as shown in Figure 7.1. The rotor of the IMG consists of a

cylindrical rotor carrier and laminated steel stacks. Each steel stack is provided with

interior mounted permanent magnets. Those magnetic steel stacks are assembled to

the rotor carrier through defined interlocking angle.

A modeled schema of this plant is represented in Figure 7.2. The system is composed

of two main branches, respectively dedicated to the assembly and magnetization of the

rotor and to the stator production. The assembly of these two sub-assemblies takes

place at a downstream assembly stage and the complete engine is produced. The as-

sembly key characteristics of the engine is the magnetic moment which is measured and

if it is observed to deviate more than 4% from its target value, the product is identified

as a defect to be scrapped.

The quality control of the engines currently takes place at the end of the line (EOL test-

ing), similar to the most of multi-stage production systems. The main disadvantage of

EOL inspection is the off-line inspection at the final stage of the manufacturing system,

where already all defects of the production system have been generated. Therefore, the

EOL testing prevents from any possible repair operation. To overcome this drawback

it is necessary to create solutions to reduce either defect generation or defect propaga-

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Figure 7.2: Schema of Current Manufacturing System.

tion. In this case study we focus on reducing the final assembly defect generation by

adapting the selective assembly system in the assembly station of the production line

of electrical engines.

7.2.1 Manufacturing Stages

The main focus of the analysis is on the rotor assembly. In details the system is

composed of seven main stages, dedicated to the following operations:

• M1: loading of the stacks on the pallet.

• M2,1,M2,2: two parallel stations assembling the magnets on the stacks. The sta-

tions are composed of a pick and place system for the positioning of the magnets

in their locations. Moreover, the glue is dispensed at the interfaces between the

magnets and the stacks surface. Finally, the glue is thermally treated in a single

oven for both parallel stages.

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• M3: Stack magnetization process. Each stack is centered in the magnetization

device that is produced by a supplier and currently un-controlled by Bosch. As

a matter of fact, it is treated as a black box. It is known that it works in the

saturation regime.

• M4: heating station. A rotating table carrying 4 magnetized stacks moves the

stack into a heating chamber for preparing the stack to the next assembly oper-

ation. Indeed the assembly principle is based on mechanical interference. Since

it has 4 stacks position, it could be used in the future as a sequence decoupling

stage.

• M5: assembly machine. The required number of stacks, normally varying from

5 to 10 for different product types, is taken from the heating machine and a pile

of stacks in the z axis of the machine is formed by mounting each stack on the

central shaft. This represents the core of the rotor. In the current production

line, the angle between the rotor stacks is fixed and cannot be changed by the

operators.

• M6: rotor balancing station.

• M7: rotor marking station.

The remaining stations perform the following operations:

• Mx,Mz,Mk,Mj : processes of stator assembly, not treated in detail in this case

study.

• Mg: assembling rotor and stator together.

• Mk: End-of-line (EOL) testing of final motor where several motor properties are

measured.

A new measurement devices are included at stages M3 and M5 for detection of devia-

tions in the magnetic field of a single rotor stack and the complete rotor, respectively

(MuProD [2013a,b]). In details, these actions include:

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• The development of a new sensor for the space resolved measurement of the

magnetic field of each single stack. This will result in an additional inspection

point that will be located after machine M3.

• The development of a new multi-sensor system distributed in the z axis of the

rotor, for measuring the field of each stack in the assembled rotor and check for

uniformity of the overall rotor field after stage M5.

7.2.2 Modeling Approach

The main modeling assumptions which are applied for performance evaluation model

are summarized below:

1. Since buffers B1.1 and B1.2 are provided with the same stacks from the upstream

machine M1, they are considered as a single buffer transferring the stacks to both down-

stream machines.

2. According to the current configuration of Bosch production line, both machines M2.1

and M2.2 are performing the same operation, assembling the magnets on the stacks.

Therefore they are considered as two parallel machines in the model.

3. Parallel machines M2.1 and M2.2 are fed by two out-of-line buffers, B0.1 and B0.2, in

which magnets raw part are stored. The capacity of those buffers is considered infinite

and therefore the magnets raw parts are always available.

4. Buffer B4 behaves a bit different compared to other buffers of the line. Since 5

magnetized stacks are required to be assembled in the downstream machine M5, the

buffer B4 is required to have the availability at least of 5 magnetized stacks.

5. Having assembled the rotor at station M5, all the other downstream machines are

aggregated together, since there is no buffer after station M5.

6. The machine M5 is, in theory, an assembly machine. But, since there is no buffer

downstream, the approximation of the assembly operation is provided by considering

the throughput as the number of coupled stacks per minute.

7. The machines Mx, Mz, Mk and Mj , which create the stator assembly line are not

modeled in this case study.

From the available information, it is realized that the system yield is affected by two

machines, i.e. M3 and M5. The schema reported in Figure 7.3, shows the transforma-

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Figure 7.3: Approximation of the original Bosch layout with a multistage process-chain

model.

tion of the original Bosch line model to an approximated equivalent production line.

In order to analytically approximate the performance of the current manufacturing

model, the details about the machines and buffers, as provided by Bosch MuProD

[2013c], are reported in Table 7.1 and Table 7.2 respectively.

Some considerations are provided in the following:

1. M1: The loading of the stacks to the pallets is operated in this machine. It is

subject to a unique operational failure. When the machine is operational, it takes

0.15 minutes to process a stack. Moreover, the machine fails on average every

480 minutes and takes 0.15 minutes to get repaired.

2. B1,2: This buffer is obtained from the coupled buffers B1.1 and B1.2 from the

original model in Figure 7.2. The capacity of the buffer is considered finite and

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Machine MTTF [min] MTTR [min] Cycle time [min] Production unit

M1 480 0.15 0.15 Stack

M2 300 10 1.8 Stack

M3 160 1 0.69 Stack

M4 175200 480 0.667 Stack

M5 28800 150 0.8 Stack

Table 7.1: Mean time to failure, mean time to repair and cycle time of the machines.

Buffer Capacity

B1,2 5

B2,3 40

B3,4 40

B4,5 6

Table 7.2: Capacity of each buffer in the current manufacturing system[number of stacks].

equal to 5.

3. M2: As previously mentioned, machines M2.1 and M2.2 of Figure 7.3 are consid-

ered as parallel machines. Moreover, they are subject to a single failure mode

machines. The processing rate in each machine is 1.8 minutes per stack. About

the reliability, each machine fails on average every 300 minutes and gets repaired

in 10 minutes.

4. M3, M4 and M5 are modeled as single failure mode in the system (data in Table

7.1).

7.2.3 Characterization of the quality parameters

In terms of quality, the problem associated to the spatial magnetization of the rotor

arises from the magnet assembly performed at M2 and the stack magnetization oper-

ations performed at M3 (Colledani et al. [2013]). It gets visible at the new inspection

station designed by Marposs and Bosch and located at M3. Based on prior analysis,

the fraction of stacks featuring non-uniform magnetization is estimated at 6%. There-

fore, considering the generated magnet flux intensity of the coupled stacks as the key

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7.3. NEW CONFIGURATIONS FOR ROTOR MANUFACTURINGLINE

quality characteristic of the final assembly of rotors, the system yield of the current

manufacturing system, Ysystem, is approximately 94%.

7.3 New Configurations For Rotor Manufacturing Line

The advantage of adopting the selective assembly system is to improve the quality of

the assembled rotor, by compensating the stacks variability. The assembled key quality

characteristic in the following experiments is the sum of the total magnetic flux inten-

sity obtained from coupled stacks. The objective of the selective assembly is to make

this value as close as possible to the target value. In order to obtain the target value,

selective assembly proposes to match the weaker stacks with stronger ones, so that the

variation in the total magnetic flux intensity can be canceled out (the comparison of

normal assembly and selective assembly is provided in Figure 7.4). The system per-

formance of current manufacturing line is then compared with the performance of new

configuration system included selective assembly system. In the following sections the

analysis of the new proposed configurations are provided.

The analyzed configurations to Bosch electrical engine manufacturing includes the se-

lective assembly system with number of quality classes that varies from 2 to 8. In

these particular configurations, number of buffers of the selective assembly cell is equal

to the number of classes, for instance, the selective assembly system of two classes is

connected to two buffers while in the generic selective assembly model, the system of

two classes is identified by four buffers. This is because in this manufacturing system

the final assembly is composed of two similar sub-assemblies that share the same man-

ufacturing machine, while in the generic model each sub-assembly is manufactured in

the dedicated manufacturing machine.

7.3.1 Selective assembly with two quality classes connected to two

buffers.

The selective assembly in this case classifies the measured stacks in two quality classes.

One class is composed of weaker stacks with the sum of the total magnetic flux inten-

sity lower that the target value (39261.6 [Wb]). The second class contains stacks with

stronger magnetization, i.e. with a value of the total magnetic flux intensity greater

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Figure 7.4: Selective Assembly of stacks: schematic view.

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Figure 7.5: Proposed configuration: Selective assembly system with two classes.

than 39261.6 [Wb]. The assembly machine selects one weaker and one stronger stack in

order to realize a coupled group of two stacks that has a sum of total magnetic fluxes

closer to a target value of 78523.2 [Wb]. The proposed configuration of two quality

classes is depicted in Figure 7.5. This must be noticed that in the proposed configura-

tions including the selective assembly, as the number of quality classes increases, the

total buffer size of the corresponding buffer remains the same as the baseline configu-

ration, which is 40 stacks.

As shown in Figure 7.6 the selective assembly system (blue distribution) was able to

perform better in providing assembled stacks which have lower variability if compared

to the no selective assembly system (red distribution). The corresponding variance us-

ing the selective assembly system of two classes is 6074.1 [Wb2], which implies 63.15%

reduction of variance comparing to 16486.9 [Wb2] which is obtained by normal assembly.

It is worthy to note that the selective assembly can smooth the input variability. The

variance of the single stack total magnetic flux intensity was 8393.37 [Wb] by Monte

Carlo Simulation. The effect of this policy on the output distribution is estimated by

simulating 10,000 stacks, which are used to realize 5,000 assembled stacks. The same

analysis is repeated while assembling according to the order of arrival of the stacks.

This must be noticed that the reduction of variance of generated magnetic flux does not

directly imply the system yield improvement. We will discuss the system performance

improvement in the next section, after introducing each configuration.

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Figure 7.6: Distribution of the magnetic flux intensity of the coupled stacks applying the

selective assembly with two quality classes and normal assembly strategy.

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Figure 7.7: Proposed configuration: Selective assembly system with four classes.

7.3.2 Selective assembly with four quality classes connected to four

buffers.

The selective assembly system in this configuration classifies measured single stacks

into four classes. Each class is connected to one dedicated buffer and the boundaries

of these classed are reported in Table 7.3 (the equal probability partitioning scheme is

considered). The system topology of the proposed configuration is depicted in Figure

7.7.

Equal Probability Scheme For Four Classes

LSL USL

Class 1 38986,17 39199,20999

Class 2 39199,20999 39261

Class 3 39261 39322,79001

Class 4 39322,79001 39535,83

Table 7.3: Equal probability partitioning scheme for four quality classes.

The distribution of total magnetic flux intensity by applying the selective assembly

system of four quality classes (blue distribution in Figure 7.9) features less variability if

compared to the normal assembly strategy, shown in blue. The corresponding variance

with selective assembly is 2734.6 [Wb2]. This is lowered if compared to the value

obtained by using only two classes (6074.1 [Wb2]). It can be noticed that the addition

of two classes lowers the variance of the assembly process by more than a half (54.97%).

The four class selective assembly policy reduces the variance by 84% if compared to

the no-selective assembly policy.

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selective assembly with four quality classes and normal assembly strategy.

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selective assembly with six quality classes and normal assembly strategy.

7.3.3 Selective assembly with six quality classes connected to six

buffers.

The selective assembly system in this case classifies measured single stacks into six

classes. Each class is connected to a dedicated buffer and the boundaries of these classed

are reported in Table 7.4 (the equal probability partitioning scheme is considered).

The system topology of the proposed configuration is depicted in Figure 7.10. The

variance of the generated magnetic flux intensity in the selective assembly system of

6 quality class is 1345 [Wb2], which is reduced by 103% respecting the no-selective

assembly configuration. The distribution of total magnetic flux intensity by applying

the selective assembly system of four quality classes (blue distribution in Figure 7.9)

features less variability if compared to the normal assembly strategy, shown in blue.

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Figure 7.10: Proposed configuration: Selective assembly system with six classes.

Equal Probability Scheme For Six Classes

LSL USL

Class 1 38986,17 39172,35006

Class 2 39172,35006 39221,54023

Class 3 39221,54023 39261

Class 4 39261 39300,45901

Class 5 39300,45901 39349,62537

Class 6 39349,62537 39535,83

Table 7.4: Equal probability partitioning scheme for six quality classes.

7.3.4 Selective assembly with eight quality classes connected to eight

buffers

The selective assembly in this case classifies the laminated stacks into eight equal prob-

ability partitioned classes. As before, the classes are connected to dedicated buffers as

shown in Figure 7.11. Table ?? shows the equal probability partitions of corresponding

selective assembly with eight quality classes.

The corresponding variance of the assembled stacks from simulated result of selective

assembly of eight quality classes is 1279.1[Wb2], as illustrated in Figure 7.12. The

obtained variance is reduced by 92.25% comparing to the no-selective assembly system.

7.3.5 Comparison of the four analyzed configurations

By comparing the four configurations, it can be observed that the output distribution

(the distribution of the coupled stacks) is getting more centralized to the target value

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Figure 7.11: Proposed configuration: Selective assembly system with eight classes.

Figure 7.12: Distribution of the magnetic flux intensity of the coupled stacks applying

the selective assembly with eight quality classes and normal assembly strategy.

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Equal Probability Scheme For Eight Classes

LSL USL

Class 1 38986,17 39155,61649

Class 2 39155,61649 39199,20999

Class 3 39199,20999 39231,80945

Class 4 39231,80945 39261

Class 5 39261 39290,19055

Class 6 39290,19055 39322,79001

Class 7 39322,79001 39366,38351

Class 8 39366,38351 39535,83

Table 7.5: Equal probability partitioning scheme for eight quality classes.

with less variance as the number of quality classes is increased. The reduction of the

assembled stacks variance as the number of quality classes increase is shown in Figure

7.13. However, it should be also noticed that by increasing the number of classes the

complexity of the production logistics increases and higher fraction of surplus, non-

matched, assemblies are generated. In the other words, due to the accumulated surplus

sub-assemblies in the buffers with limited capacities, the manufacturing machines have

to discard with higher rate as the number of classes increases. This results in lower

level of total throughput. Therefore, in order to compare effectively the proposed con-

figurations, these competing effects should be studied under an integrated framework

of quality and production logistic performance. For this reason, we have extend our

simulation model of selective assembly system for more classes, integrated in the corre-

sponding manufacturing system. The simulation model was developed considering the

same assumption as those adopted for developing the approximate analytical method.

Beside, the analytical model can be extended with the same proposed framework as

two quality classes for more quality classes.

The obtained generic performance measures of the proposed selective assembly config-

urations are shown in Table 7.6. This results are obtained by running the simulation

model for 10 replications of 1,000,000 time units for each configuration. Also, 100,000

time unit is considered for the warm-up period. The 95% confidence interval for each

performance measure is provided in the Table 7.6.

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Figure 7.13: Reduction of variance with increasing number of quality classes.

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N. of Classes TH Eff CI TH Tot. CI WIP CI System Yield CIDiscard

rateCI

No Selective

Assembly0,50811 0,003 0,53593 0,002 18,6 1,16 0,94807 0,002 0 0

2 0,51922 0,001 0,52068 0,001 15 1,90 0,99721 0.0004 0,0252 0,002

4 0,51193 0,002 0,51212 0,002 17,4 2,42 0,99962 0.0001 0,04924 0,002

6 0,49868 0,005 0,49876 0,005 14,6 2,85 0,99985 0.009 0,07438 0,005

8 0,48721 0,004 0,48727 0,004 15,4 4,52 0,99989 0.000 0,0947 0,002

Table 7.6: Performance measures of the proposed Selective Assembly configurations.

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Consider the total throughput of the system as the number of classes increases, de-

picted in Figure 7.14. As it can be noticed, the total production rate is decreasing as

the number of quality classes increases. This is because as the number of quality classes

increases the complexity of the logistic system increases as well. The complexity of the

logistic system with the finite buffer capacities causes the manufacturing machine blocks

more and due to discard policy, manufacturing machine discards more sub-assemblies

(As it is shown in Figure 7.15). On the other hand, the assembly machine starves more

frequent as the number of quality classes increases due to the lowered level of available

coupled buffers. Therefore, discarding more sub-assemblies in addition to more star-

vation probability of the assembly machine, as the number of quality classes increases,

leads to the reduced total throughput.

Figure 7.14: Throughput total as the number of quality class increases.

Although the total throughput is decreasing, but the system yield is increasing as the

number of quality classes increases, as it is shown in Figure 7.16. Therefore, the conse-

quent effective throughput of the system has a monotone increasingly behavior guided

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Figure 7.15: Discard Rate as the number of quality class increases.

by the reduced total throughput and the contrasting effect of increased yield, as shown

in Figure 7.17.

As it can be observed in Figure 7.17, the effective throughput behavior differs from

the decreasingly curve representing the total throughput of the system, and it presents

a maximum. This means that there exist an optimal number of quality classes that

maximizes the throughput of the conforming assemblies. This suggests that, according

to the number of quality classes of selective assembly and the resulting quality and

productivity parameters, the system designer should configure the selective assembly

system to reach the maximum of effective throughput curve, without considering the

system yield and total throughput behavior separately. In addition, we showed in Fig-

ure 7.13 that the variance of the generated magnetic flux intensity decreases as the

number of quality classes increase, but by observing the effective throughput we real-

ized that the optimal configuration is the selective assembly system with two quality

classes and considering only the reduced variance of the final assembly key character-

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7.4. THE EFFECT OF FINAL ASSEMBLY KEY CHARACTERISTICTOLERANCE TIGHTENING ON THE EFFECTIVE THROUGHPUT

Figure 7.16: System Yield as the number of quality class increases.

istic obtains the configuration that sub-perform the optimal configuration.

7.4 The Effect of Final Assembly Key Characteristic Tol-

erance Tightening on The Effective Throughput

In order to demonstrate the benefits of the selective assembly comparing to the normal

assembly, we also tested the system performance in the scenario that the requested

tolerance on the final product key characteristic is tightened. This is important be-

cause often tighter tolerances on the final assembly key characteristic leads to the more

performing products. On the other hand, the more tightened tolerance causes the lower

level of the system yield and the effective throughput, while the configuration is fixed.

Therefore, it is needed to jointly consider the effect of quality (tighter tolerance on

the final assembly key characteristic) and the production logistic performance on the

manufacturing system performance under different system configurations.

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Figure 7.17: Effective Throughput as the number of quality class increases.

The manufacturing system characteristics, i.e., the machine reliability data and the

total buffer capacities, are the same as the baseline manufacturing system for both the

normal assembly and the selective assembly systems. Table 7.7 provides the considered

tolerance limits for the experiments.

7.4.1 Experiments Results

In Table 7.8, 7.9 and 7.10, the behavior of the baseline system configuration (no se-

lective assembly) is compared with the proposed selective assembly system with 2, 4,

Tolerance [Wb]

Tol. Std. 503,32

Tol./2 251,66

Tol./4 125,83

Tol./6 83,886

Table 7.7: Tested Tolerance Limits.

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7.4. THE EFFECT OF FINAL ASSEMBLY KEY CHARACTERISTICTOLERANCE TIGHTENING ON THE EFFECTIVE THROUGHPUT

6 and 8 quality classes when the tolerance limit on the key characteristic of the final

assembly (the generated magnetic flux intensity of a coupled stacks) is divided by 2,

4, and 6, respectively. Figure 7.18 represents the effect of the tolerance tightening on

the effective throughput of the baseline manufacturing system as well as the proposed

selective assembly systems.

As it is mentioned earlier, for the case of standard tolerance on the final assembly key

characteristic, denoted as T, the proposed selective assembly with two quality classes

outperform the baseline (no selective assembly) system by 2.18%, while the selective

assembly systems with 4, 6 and 8 quality classes sub-perform the baseline manufacturing

system. However, when the tolerance is tightened to T/2, the 4, 6 and 8 quality class

selective assembly systems improve the effective throughput approximately by 37%,

and the two class selective assembly outperform the baseline manufacturing system by

26.85%. As the tolerance become tighter the positive effect on the effective throughput

become even more visible by the number of quality classes. For instance, T/6 the

effective throughput is improved by 66,1%, 170,6%, 217,8% and 236,7% for 2, 4, 6,

and 8 quality classes, respectively. Therefore, the results highlight the fact that as the

tolerances on the final assembly becomes tighter, selective assembly system with more

quality classes are out-performing more effectively. Even though more quality classes

reduces significantly the total throughput but the contrasting effect of the obtained

yield compensates the effective throughput.

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T/2 TH Tot CI TH Eff CI WIP CI Yield CI Discard Rate CI

No Selective 0,53593 0,002 0,35794 0,003 18,6 7,16 0,66788 0,005 0 0

2 Class 0,51062 0,003 0,45405 0,003 11,4 2,57 0,88923 0,001 0,04888 0,003

4 Class 0,50843 0,001 0,49386 0,002 12,8 3,76 0,97133 0,001 0,0539 0,002

6 Class 0,50456 0,004 0,49761 0,004 15,6 7,58 0,98624 0,001 0,06057 0,006

8 Class 0,50634 0,005 0,50182 0,005 19,8 5,91 0,99106 0,0007 0,05556 0,004

Table 7.8: Performance Measures for the tolerance limit divided by 2 (T/2).


No Selective 0,53593 0,002 0,19911 0,002 18,6 1,16 0,37152 0,004 0 0

2 Class 0,51062 0,003 0,30917 0,001 11,4 2,57 0,60549 0,004 0,04888 0,003

4 Class 0,50843 0,001 0,43408 0,001 12,8 3,76 0,85376 0,002 0,0539 0,002

6 Class 0,50456 0,004 0,46263 0,004 15,6 1,58 0,91691 0,0009 0,06057 0,006

8 Class 0,50634 0,005 0,47727 0,005 19,8 5,91 0,94257 0,001 0,05556 0,004



No Selective 0,53593 0,002 0,13569 0,001 18,6 1,16 0,25317 0,002 0 0

2 Class 0,51062 0,003 0,22539 0,002 11,4 2,57 0,44142 0,005 0,04888 0,003

4 Class 0,50843 0,001 0,36727 0,000 12,8 3,76 0,72237 0,003 0,0539 0,002

6 Class 0,50456 0,004 0,43132 0,003 15,6 1,58 0,85485 0,003 0,06057 0,006

8 Class 0,50634 0,005 0,45689 0,005 19,8 5,91 0,90232 0,001 0,05556 0,004


160

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Figure 7.18: Effect of tightening the tolerance on TH Eff.

161


162

8

Selective Assembly Application

in Automotive Industry: Door

Assembly in Jaguar and Land

Rover Company

In this section we describe the application of the selective assembly system in auto-

motive industries. As mentioned earlier, selective assembly has been suggested as an

effective approach to support tight dimensional control of part-to-part gap during re-

mote laser welding operations in the automotive industry (FP7-2011-NMP-ICT-FoF

[2012]). In this application, a tight gap control is essential to ensure the high quality of

the produced stitch, in terms of mechanical properties and corrosion resistance. Typi-

cally, the gap cannot be smaller the 0.1[mm] while processing zinc coated sheet metals.

The risk of a smaller gap is the explosion or ejection of molten weld metal caused by

the escape of trapped high pressurized zinc vapor. Moreover, the gap cannot be larger

than 0.3[mm]. The reason is the risk of lack of fusion and insufficient penetration of

the stitch in the components (Steen [1993]). Selective assembly can classify compliant

sheet metals after forming in order to have a homogeneous gap between components

during the welding process, contributing to high quality welding. This requires the

inspection-based characterization of the geometrical variation of the metallic sheets.

The measured data can be characterized by statistical modal analysis (Ceglarek and

Huang [2007]). In this case study, the remote laser welding is proposed to be applied in

163

8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY

the manufacturing line of door production in Jaguar and Land Rover (JLR) company

instead of the current resistant spot welding technology. The data, results and analysis

of the proposed configurations are reported in deliverable of an EU project, Remote

Laser Welding System Navigator for Eco & Resilient Automotive Factories. In the

following, first we describe the current manufacturing system and the corresponding

manufacturing model, then we will discuss the model of the proposed configuration

which includes the selective assembly system. Finally, we compare the results of the

proposed configuration with that of the current configuration.

8.1 JLR Door Manufacturing System Description

The studied manufacturing system is the assembly line for the front door (left side

and right side) of one of the company’s vehicles. The current manufacturing system

is assembling the door by applying the Resistant Spot Welding, denoted also as RSW.

The material of the sub-assemblies to be welded into a door for a door variant model

is shown in Figure 8.1. Figure 8.2 illustrate the precedence diagram representing the

sub-assemblies precedence for assembly operation through the line. Materials used for

the door assembly are generally, zinc galvanized mild steels and hot formed boron for

the impact beam.

The schematic layout which is shown in Figure 8.3 describes the stations, the work

process flow between stations which starts from Station 100 and ends with Station 320.

The mathematical modeled layout describes the work stations can be best summarized

in Table 8.1 and Figure 8.4. The door assembly process generally involves loading

process, welding, hemming and curing process before it is assembled onto the Body in

White (BIW). It is operated by a total of 4 operators located in the 3 loading and 1

unloading stations to load the sub-assemblies onto the fixtures at Station 100, 140, 200

and 320 of the production line. Total of 95 spot weld location are required per door.

The sequence of parts joint according to process and stations can be understood from

Figure 8.1. The longest process is the hemming process which is 129 seconds per unit

door. Table 8.1 illustrates the equipment, welds and cycle time of each station of the

door process.

164

8.1. JLR DOOR MANUFACTURING SYSTEM DESCRIPTION

Figure 8.1: Current Assembly Sequence of Front door for model.

165


S1

3

5

9

9

4

S2

2

6

8

140

100110120

S3

160

220190

150

S4

1

300

210200

310

320

Usage/Product Component ID Component Name

1 1 PNL DR O/S R/LH (3 Dr )

1 2 CHAN FRT DR WDO GL R/LH (Common 3 Dr/5Dr )

1 3 PNL FRT DR I/S R/LH (3 Dr)

1 4 REINF DR I/S PNL OPNG R/LH (3 Dr )

1 5 REINF DR I/S PNL @ LAT R/LH (Common 3 Dr/5Dr )

1 6 REINF FRT DR O/S PNL @ BELR/LH (3 Dr )

1 7 PLT ASY DR HGE (COMMON 3 & 5 Dr)

1 8 STRN DR O/S PNL R/LH (3 Dr )

2 9 PLT ASY DR HGE (COMMON 3 & 5 Dr)

JLRZ18_3Dr_Model

Precedence Diagram

Figure 8.2: Precedence Diagram for the front door assembly line for the current config-

uration.

166

8.1

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NFigure 8.3: Schematic layout of current manufacturing system for assembly line of right and left front door (identical systems).

167


Figure 8.4: Current manufacturing system model of the door assembly system.

In this section we explain the synthetic description of operations in Front Door As-

sembly line in more details. The operations synthetic is summerized also in Figure

8.5.

Station 100. Operator 1 picks up the inner panel from the corresponding racks and

loads to geo welding. Then, Operator 1 pushes the start button that starts the clamp

and performs pin engagement. Operator 1 loads and clamps each of the other 5 parts

one at a time. When the loading of the 6 parts is finished, he pushes a start button to

close the shutter door and he moves to station 140. The start button causes the robot

100R1 to begin tack welding when tack welding finishes 100R2 unloads the assembly

from geo station and cones the latch plate.

Station 110. Robot 100R2 moves to station 110 from station 100 in order to load

the assembled panel the geo of Station 110 and after loading comes back to Station

100. Afterward, robot 110R1 starts tack welding the while turn table position the

part properly. After tack welding, clamps and pins are automatically retracted. 120R1

moves from next station (station120) to this station in order to unload the part to

station 120.

Station 120. 120R1 re-spot welds and moves the inner panel to station 140.

Station 140. While stations Stn110 and Stn120 was working on inner panel OP1

who previously worked in Station 100 left there, loads three more parts, Glass channel,

Waist rail and Intrusion beam. The roller shutter door closes after OP1 complete

loading and OP1 goes back to Station 100. Robot 140R1 unloads these three parts and

moves them to Station 150.

168


Figure 8.5: Graphical operation synthetic description

169


Station 150. Two paths come to this station, the first from Station 140 (three

additional parts) and then Station 120 (Inner panel). 150R2 starts geo welding (17

spots) and 150R1 joins into the geo welding after the first 8 spots. 150R1 and 150R2

move to home position, and then 150R3 unloads inner sub assembly from Station 150

in order to load to Station 160 which is deposit. [In this stage inner panel is almost

complete and the only operation left in anti-flutter operation which will be performed

before the hemming process which joints inner panel and outer panel.]

Station 160. In each cycle time, each inner sub-assembly panel will be loaded to

deposit by 150R3 and spends around 23 Seconds there (17% of Cycle Time). Robot

140R1 unloads inner sub-assembly panel and moves to Station 190.

Station 190. This station includes ”PUT DOWN ” and ”Date Stamp”. First,

140R1 loads the PUT DOWN with the inner panel and then 190R1 unloads from PUT

DOWN (2 seconds after loading by 140R1). 190R1 applies Date Stamp and moves to

Station 220 which is the next station for inner panel before joining the outer panel.

Station 220. 190R1 applies the anti-flutter operations to three welding beads.

Station 200 (outer panel loading). Operator 2 loads the outer panel to the station

from the corresponding rack. He pushes the start button which closes the roller shutter

door. Then, OP2 goes to Station 320. Robot 200R1 unloads the part from Stn200 in

order to go to Station 210.

Station 210. Robot 200R1 applies hem sealer on two different position of the outer

panel and moves to Stn300.

Station 300. Inner sub-assembly panel comes to this station by means of 200R1

and outer panel by means of 190R1 from their respecting manufacturing flow. 300R1

performs hemming, which results in joining two panels and moves the unified part to

Station 310.

170


Station 310. 300R1 loads the curing machine and goes back to its home position.

After the curing operation is done, 310R1 unloads the curing machine and loads the

exit conveyor.

Station 320. Operator 2 who walked to this station after loading the outer panel in

Station 200 performs sealer wiping and loads the final part to the completed part rack

and turns back to Station 200.

171

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Equipment Welds

Station Description Turntable/

Fixture

Handling/

Hemming

Robot

Weld

Robot

PED

Gun

Tack

Weld

Spot

Weld

Cycle

Time

Operator

No.

100 Loading 1 1 1 10 121 1

110 RSW 1 1 13 12 128

120 RSW 1 1 30 95

140 Loading 1 2 44 1

150 RSW 1 2 19 11 118

160 Loading 1 38

190 Buffer 31

200 Loading 1 28

210 Adhesive 1 1 31

220 Anti-Flutter 1 1 21

300 Hemming 1 3 129

310 Curling 2 1 112

320 Unloading, QC 116 2

Total 9 10 4 3 42 53 4

Table 8.1: Current Manufacturing System Station Description.

172

8.2. THE NEW CONFIGURATION OF ASSEMBLY SYSTEM:APPLICATION OF REMOTE LASER WELDING

Table 8.2 represents the analyzed data from the company data base to extract the re-

quired parameters; p is the failure rate of the station, r is the repair rate of the station,

CT is the cycle time of the station, mu is the processing rate of the station, i.e. 1/CT ,

the iso-throughput is the isolated production rate of the station, i.e. the production

rate the station would have if it was completely isolated from the rest of the line, i.e.,

without considering the impact of the neighboring machines and buffers, and e is the

isolated technical efficiency of the station, i.e., the fraction of time the machine is op-

erational, again if not impeded by other machines in the system.

The current configuration of the mentioned system, only involving RSW technology

was modeled and evaluated with the analytical method, grounding on the reliability

data which is provided by the robots manufacturer while designing their plants. The

studied manufacturing system currently includes two identical systems, one dedicated

to the production of front left doors, and one dedicated to the production of front

right doors. The total throughput of the system under the current configuration is

0.4553 part/min, corresponding to a 27.318 job per hour [JPH]. This follows 27.318

front right door per hour and 27.318 front left door per hour. According to the quality

control sector of the company, all the assembled part are conforming. This means the

system yield is equal to 1. Therefore, the effective throughput of the system is equal

to the total throughput and its equal to 0.4553 for each side front door. This has to

be considered as the target throughput for the proposed configuration of this system,

since the current configuration is able to meet the requirements of the body production

line. The system bottleneck (station with the smallest isolated production rate) is the

hamming station (Station 300). Its isolated throughput (0.4631 parts/min) represents

the maximum possible achievable production rate in the system.

8.2 The New Configuration of Assembly System: Appli-

cation of Remote Laser Welding

The robot supplier of the JLR company proposed to apply the remote laser welding

technology for some of the important joints of the door during the assembly. In the

proposed configuration number of robots are reduced from 14 to 8 and the design of

sub-assemblies slightly changed. In fact, the resistant spot welding technology is not

173


Station ID p r CT mu iso mu e

1 ST 100 0,001313 0,2 1,26 0,7937 0,7885 0,9935

2 ST 110 0,00076 0,2 1,7 0,577 0,5748 0,9962

3 ST 120 0,000791 0,2 1,94 0,5155 0,5134 0,9961

4 ST 140 0,000553 0,2 0,6 1,7857 1,7808 0,9972

5 ST 150 0,001965 0,2 2,03 0,4926 0,4878 0,9903

6 ST 190+220 0,000553 0,2 0,85 1,1765 1,1732 0,9972

7 ST 200+210 0,000553 0,2 0,908 1,1013 1,0983 0,9972

8 ST 300 0,000872 0,2 2,15 0,4651 0,4631 0,9957

9 ST 310 0,000715 0,2 1,733 0,577 0,575 0,9964

10 ST 320 0,000207 0,2 1,556 0,6427 0,642 0,999

Table 8.2: Summary of parameters of the current manufacturing system, adopted for

analytical performance measurement method.

completely removed, but the new configuration proposes the hybrid system including

both resistant spot welding and the remote laser welding. The assembly sequence is

changed. The precedence diagram represented in Figure 8.6 shows the new assembly

sequence of sub-assemblies.

In the new proposal of the system, the Remote Laser Welding (RLW) station is shared

between the two part types, the left front door and the right front door. The RLW

robot is welding the right front door in each cycle time and then it turns to left front

door line, welding the left door. Due to the fast processing rate of the RLW robot,

before the next sub-assembly of the right side appears in the RLW station, the RLW

robot finishes the left door and returns to the right side again. In this thesis we focused

only on the production system of the right front door. The proposed layout is presented

in Figure 8.7. The new configuration is designed to be run by two operators, one ded-

icated to each part type (left and right front doors). The synthetic feature of the new

configuration is reported in Table 8.4. The proposed configuration saves 6 robots for

each of the symmetric line, which is 12 robots for the whole system. Therefore, the

resulting system saves 40% in terms of number of robots.

The parameters of the stations which characterizes the machines reliability data is pro-

174


Figure 8.6: Precedence Diagram for the front door assembly line for the new configuration.

175


vided in Table 8.3. The manufacturing model of the proposed hybrid configuration,

including the RSW and RLW, is represented in Figure 8.8. The considered system is

shown by the red squared line, which is the right front door assembly system. The

performance of the current system is evaluated by the analytical model based on de-

composition method which supports the performance evaluation of the assembly system

with continuous flow of material and continuous time. The obtained results are pro-

vided in Table 8.6. As it can be noticed, although the robots are reduced by 40% in

both lines, but as it can be noticed the effective throughput is lower than the target

effective throughput, which is 0.4553 [part/min]. Therefore, we have applied the selec-

tive assembly method for RLW assembly station to improve the effective throughput

of the proposed configuration.

176


Station ID

Fail-

ure

Modes

p r CT [min] mu e iso e

ST 1 1 0,00022 0,25575 2,08333 0,48000 0,99898 0,47951

2 0,00002 0,25083

3 0,00005 0,46371

4 0,00172 1,00000

ST 2 1 0,00014 0,27822 2,03333 0,49180 0,99949 0,49155

ST 3 1 0,00048 0,25575 1,46667 0,68182 0,99951 0,68148

2 0,00004 0,37097

3 0,00028 1,00000

RLW 1 0,00155 0,28536 1,85000 0,54054 0,99814 0,53954

2 0,00002 0,25083

3 0,00006 0,33387

4 0,00007 0,45240

5 0,00007 0,25575

6 0,00153 0,20000

ST 5 1 0,00050 0,27822 1,93333 0,51724 0,99937 0,51692

2 0,00030 0,25575

3 0,00010 0,19787

4 0,00003 0,37097

5 0,00001 0,30242

6 0,00008 0,21078

ST 200+210 1 0,00055 0,20000 0,90800 1,10132 0,99724 1,09828

ST 300 1 0,00087 0,20000 2,15000 0,46512 0,99566 0,46310

ST 310 1 0,00072 0,20000 1,73300 0,57703 0,99644 0,57498

ST 320 1 0,00021 0,20000 1,55600 0,64267 0,99897 0,64201

Table 8.3: Summary of parameters of the proposed manufacturing system, adopted for

analytical performance measurement method

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Figure 8.7: The layout representing the new hybrid configuration.

178

8.2

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Activity Cycle Description Begin Duration [sec.] End

Station 100

Smart Laser Laser Welding RH door (56 stitches) 0,0 37,0 37,0

Smart Laser Laser Dimpling RH door (168 dimples) 37,0 27,0 64,0

Smart Laser Laser Welding LH door(56 stitches) 64,0 37,0 101,0

Smart Laser Laser Dimpling LH door (168 dimples) 101,0 27,0 128,0

Table Turn 180 0,0 5,0 5,0

Dimple fixture Open 5,0 4,0 9,0

120 R1 Unload parts from St 140 welding fixture 9,0 8,0 17,0

120 R1 Load parts on st 140 welding fixture 17,0 10,0 27,0

120 R1 Load parts to St 150 27,0 10,0 37,0

100 R1 Unload inner panel dimpled from st 140 dimple fixture 9,0 8,0 17,0

100 R1 Load inner panel on st 140 dimple fixture 17,0 10,0 27,0

100 R1 Load inner panel dimpled on st 140 welding fixture 27,0 8,0 35,0

Dimple fixture Close 35,0 4,0 39,0

Table Turn 180 39,0 17,0 56,0

100 R1 Change tool 35,0 19,0 54,0

100 R1 Welding respot (5 WS) OP130 54,0 15,0 69,0

100 R1 Move to st 110 69,0 2,0 71,0

100 R1 Welding geo spot (9 WS) 71,0 27,0 98,0

100 R1 Change tool 98,0 19,0 117,0

100 R1 Move to st 100 117,0 2,0 119,0

100 R1 Unload parts from loads St 100 119,0 8,0 127,0

100 R1 Move to st 140 127,0 2,0 129,0

120 R1 Move to st 120 37,0 2,0 39,0

120 R1 Unload parts from St 120 39,0 10,0 49,0

120 R1 Move to st 150 49,0 2,0 51,0

120 R1 Unload parts from St 150 69,0 8,0 77,0

179

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120 R1 Move to St 160 & Coning 77,0 16,0 93,0

120 R1 Move to St 170 Untiflutter (1020mm) 93,0 21,0 114,0

120 R1 Move and load on st 180 114,0 11,0 125,0

120 R1 Move to st 140 125,0 3,0 128,0

Station 120

OP1 Load 4 parts 0,0 32,0 32,0

OP1 Push button 32,0 2,0 34,0

OP1 Walk to st 110 34,0 4,0 38,0

Station 110

OP1 Load 3 parts 38,0 24,0 62,0


OP1 Walk to st 100 64,0 4,0 68,0

Table Turn 180 64,0 5,0 69,0

Table Turn 180 98,0 5,0 103,0

OP1 Unload part 103,0 8,0 111,0

OP1 Push button 111,0 0,0 111,0

OP1 Walk to st 120 111,0 4,0 115,0

Station 100

OP1 Load 1 parts 68,0 8,0 76,0


OP1 Walk to st 110 78,0 4,0 82,0

Table 8.4: Operation Synthetic of the new hybrid proposal including both RLW and RSW

180

8.3. THE NEW CONFIGURATION OF HYBRID SYSTEMINCLUDING SELECTIVE ASSEMBLY SYSTEM

Performance Measure Mean

TH Total 0,46235

TH Effective 0,35225

System Yield 0,76188

WIP 7,43

Table 8.5: Performance measures of the proposed manufacturing system with no-selective

assembly system.

8.3 The New Configuration of Hybrid System including


Although the total throughput of the proposed hybrid configuration is higher than the

target throughput, but the system yield of the proposed system is not sufficient to

generate the effective throughput as much as required by the company. Therefore we

proposed to apply the selective assembly system to improve the ratio of the conform-

ing parts, resulting in higher effective throughput. The new configuration proposes to

classify the inner panel and the halo sub-assembly (which is processed through spot

welding in station 1) according to their key quality characteristics by means of the new

measurement device. The inner panel and the halo sub-assembly will be welded by

RLW smart laser in the assembly station, which is represented in Figure 8.9.

In order to classify the sub-assemblies we need to analyze the key characteristics of

the sub-assemblies that influence the laser welded stitches quality. Within the RLW

process the main source of error have been identified which is the part induced errors

due to the fact that the sheet-metal parts (both sub-assemblies) are manufactured by

stamping/forming processes. Manufacturers using traditional process control charts

to monitor their sheet metal stamping processes often encounter out-of-control signals

indicating that the process mean has changed. Unfortunately, a sheet metal stamping

process does not have the necessary adjustability in its process variable input settings

to allow adjusting the mean response in an out-of-control condition. Indeed, stamping

dies and presses have several input variables, such as tonnage, shut height, press par-

allelism, counterbalance pressure, nitrogen pressure in dies, press speed. Variation of

those parameters, combined together, might affect the final quality of the stamped part.

181


Figure 8.8: Proposed configuration for left front and right front door including RLW

station with normal assembly system, focusing on the right front door.

Unfortunately, stamping processes have no simple adjustment mechanisms to change

feature dimensions. Moreover, most stamping processes run out of statistical control.

Thus, manufacturers have difficulty determining the true long run process variation

and the inherent variability in die setup operations for a batch of parts. Majeske and

Hammett [2003] suggested decomposing stamping variation into three components: (I)

part-to-part, (II) batch-to-batch, and (III) within batch variation. The part-to-part

variation represents the short run variability about a given stable or trending batch

mean. The batch-to-batch variation represents the variability of the individual batch

mean between die setups. The within batch variation represents any movement of the

process mean during a given batch run.

182


Figure 8.9: Proposed configuration including the selective assembly system of two classes

for right side front door.

In industrial SPC applications, the quality of manufactured products is evaluated by

Key Quality Characteristics identified by manufacturing engineers. Traditionally, these

characteristics have been physical measures, such as dimensions or part feature loca-

tions. These dimensional quality characteristics are of fundamental importance in as-

sembly, since variation in parts may lead to significant problems during the assembly

process, resulting in poor performance of the final product. Therefore, it is vital that

each part is within the specification limits for ease of assembly; ideally, the products

quality characteristics should be as close as possible to their corresponding target val-

ues. Traditionally, the choice of the Key Quality Characteristics was restricted by the

capabilities of the available measurement technologies. For example, consider the as-

sembly of car doors, where an inadequate door fit leads to a loss of quality, possibly

characterized by excessive door closing effort, increased wind noise, and/or decreased

aesthetics. Wells et al. [2012] noted that the quality of a doors fit is a function of

dimensional variations in the doors, body openings, and fitting and hanging processes.

To assess the fitting quality, engineers must decide on what to measure on the assem-

bly and how to interpret the data. Typically, quality inspection practitioners select

between 50 and 100 sampling points per door, track these points using Coordinate

Measuring Machines (CMMs), and then apply SPC methods to assess if the observed

vehicle-to-vehicle variation is significant Wells et al. [2011]. However, these sampling

points may not capture all possible variation sources since only some gaps between the

183


door and the body are measured.

Therefore, it is important to develop SPC methods that can better monitor the qual-

ity of such complex products, especially since increased variation in product quality is

often an indication of process deterioration. For example, in RLW applications it is

crucial to determine the variation of functional features (i.e., part-to-part gap at flange

areas) in order to assess the quality of the laser welded joints.

Advanced measurement technologies provide the opportunity to collect millions of data

points, allowing for a products entire surface geometry to be represented. With this

type of data, fault detection is no longer limited by traditional measurement system

capabilities. By monitoring the entire surface geometry one can detect the occurrence

of unexpected fault patterns, i.e. faults that would not normally impact pre-set CMM

measurement points Wells et al. [2012].

Three-dimensional surface-based scanners have recently emerged as a measuring tech-

nology that can rapidly provide such information. Son et al. [2002] showed that the

current focus for 3D scanners resides in reverse engineering applications and provid-

ing one-to-one comparisons between manufactured parts and their corresponding CAD

representations. Despite the importance of such comparisons, they only provide infor-

mation for a single scanned product, rather than capturing the part-to-part or batch-

to-batch variation, which is necessary for an accurate depiction of the state of the

manufacturing process. Therefore, surface-based scanner is a promising technology to

monitor the entire surface geometry and to detect the occurrence of unexpected fault

patterns.

Due to the fact that the data regarding the sub-assemblies measurement is confidential

for the company, in this thesis we have considered the limited data for analyzing the

effect of selective assembly system without lose of generality. According to the ana-

lyzed data regarding the stitches, we found out that there is a critical stitch which is

considered as the key quality characteristic of the final assembly. In order to meet the

required tolerance on this stitch, there is a single point on each sub-assembly that is

pointed as the key characteristics of each sub-assembly. The provided measurement

184


Figure 8.10: Proposed configuration including the selective assembly system of three

classes for right side front door.

data form sampling of each sub-assemblies depicts the Gaussian distribution for the

variation regarding the nominal value. Therefore, for the process variation of each

sub-assembly we considered the Gaussian distribution based on the sampling data. For

halo sub-assembly the critical point geometry is distributed as N(0.4474, 0.0442) and

for the inner panel sub-assembly is distributed as N(0.24, 0.052). We have modeled in

simulation the proposed configuration for selective assembly of 2 classes and 3 classes.

Figure 8.10 represents the hybrid system model with selective assembly station of 3

quality classes for remote laser welding station. It must be noticed that, the total

buffer space for selective assembly of 2 classes and 3 classes is equal to that of baseline

configuration. Classification for selective assembly of 3 quality classes is based on the

equal probability approach for both sub-assemblies. Table 8.6 shows the results of the

proposed system for selective assembly of 2 classes and 3 classes. As it can be noticed

the effective throughput obtained by the proposed selective assembly with 2 quality

classes is smaller than 0.4553 [part/min], therefore we analyzed the selective assembly

system with 3 quality classes. As it can be expected, the total throughput of the system

is reduced due to the logistic complexity while the system yield is increased. As the

effect of this competing effect, the effective throughput of the proposed system with 3

quality classes is 0.4565, which is slightly higher than the target effective throughput.

185


TH Tot. CI TH Eff CI Yield CI WIP CI

2

Classes0,46219 0,0005 0,41585 0.0008 0,89975 0,00106 21,6 2,858

3

Classes0,46069 0.0009 0,4565 0,00107 0,9909 0,00128 18 4,919

Table 8.6: Performance measures of the proposed manufacturing system for selective

assembly system of 2 and 3 quality classes.

186

9

Conclusion

In this thesis we have explored and analyzed the behavior of the selective and adaptive

assembly systems in an integrated framework of quality and system logistic performance

for the first time. The system level analysis of selective assembly system is performed

through a new analytical method in addition to the developed simulation model of

the selective assembly systems. The provided results of the analytical model show the

good accuracy of the method and the modeled system comparing to the simulation re-

sults. Beside, in this thesis we proposed to apply the production adaptability strategy

to improve the system performance of selective and adaptive assembly system. The

optimal process adaptability method is provided and the system effect of such a design

has been analyzed through the simulation model. Moreover, important insights have

been derived by the application of the selective assembly system in a real case which

open new way of designing the assembly system, jointly considering the quality and the

system logistic aspects.

The main achievements and results of this thesis can be summarized in the following

key considerations:

• An innovative modeling framework for selective assembly systems that integrates

quality and production logistics features is developed. A new approximate ana-

lytical method is developed for the performance evaluation of this systems. The

provided results show that the developed method is accurate while estimating

187

9. CONCLUSION

the main system performance measures and can be used to support the design of

these complex systems in real manufacturing settings.

• The developed analytical method is applied to observe the system behavior of

the selective assembly systems when the total buffer space is increased. The

results show that although the selective assembly system provides a higher system

yield with respect to the non-selective assembly system, but it affects negatively

the total throughput of the system. It is shown that the total throughput of

the system increased as the total buffer space increases, but due to the logistic

complexity of the selective assembly system the total throughput of this system is

reduced compared to the non-selective assembly system. It is important to notice

that the negative effect of selective assembly system on the total throughput

become less evident as the total buffer space increases. The combined result

of increased yield and decreased total throughput is the remarkable increase of

the effective throughput with respect to the traditional, non-selective, assembly

system. In addition, the positive effect of the selective assembly system on the

effective throughput of the system is even more visible as the total buffer size

increases.

• In order to explore the behavior of the selective assembly system under more

quality classes, we have developed a simulation model. The results of the simula-

tion show that although the total throughput is reduced as the number of quality

classes increases, the system yield is increased, as the number of quality classes

increases. As a result of this competing effect, the effective throughput curve is

concave, it is increasing until a certain point and then it starts decreasing. Thus,

being concerned with the concave behavior of the effective throughput curve, it il-

lustrates that there is an optimal point to select for the number of quality classes.

Therefore, in order to make a proper decision for design of selective assembly

systems in terms of number of quality classes, there is an absolute need to ob-

serve the trad-off between the total throughput and the system yield through the

resulting effective throughput.

• we have analyzed and explored the behavior of the selective and adaptive assembly

systems. In particular, we have applied the process adaptation in the manufac-

turing process in order to reduce the discard rate of sub-assemblies. The proposed

188

method is modeled within the analytical performance measurement framework of

the selective assembly systems which is addressed in previous chapters. More-

over, the proposed optimal process adaptation design is addressed. Finally, we

illustrate the effect of process adaptation in system level performance of selective

and adaptive assembly systems. We have shown that the optimal process adap-

tation design can considerably reduce the WIP while increase the throughput of

the system.

• Although the process adaptations are significantly beneficial to increase the effi-

ciency of the selective assembly systems, but not all the manufacturing processes

are able to produce with several mean target values. Therefore, we proposed new

intelligent flow control policies, based on the observable system states, to handle

better the logistic complexity of the selective assembly systems in deadlock states.

The key goal of these policies is to reduce the discard rate, thus we concluded that

the proposed policies are out-performing the Discard Policy which is proposed in

the literature, considering the discard rate of sub-assemblies.

• The application and benefits of implementing selective assembly systems in pro-

duction of the electrical engines in Bosch company is shown in the chapter 7.

The results of the proposed approaches are published as deliverable of EU funded

project (MuProD [2013d]), MuProD “Innovative proactive Quality control sys-

tem for in-process multi-stage defect reduction”. We have shown that there ex-

ist an optimal number of quality classes that maximizes the throughput of the

conforming assemblies. This suggests that, according to the number of quality

classes of selective assembly and the resulting quality and productivity parame-

ters, the system designer should configure the selective assembly system to reach

the maximum of effective throughput curve, without considering the system yield

and total throughput behavior separately. In addition, we showed that the vari-

ance of the generated magnetic flux intensity decreases as the number of quality

classes increase, but by observing the effective throughput we realized that the

optimal configuration is the selective assembly system with two quality classes

and considering only the reduced variance of the final assembly key characteristic

obtains the configuration that sub-perform the optimal configuration. It is also

shown that as the tolerances on the key characteristic of final assembly becomes

189

9. CONCLUSION

tighter, selective assembly system with more quality classes are out-performing

more effectively.

• The final chapter is associated with the formalization, modeling, and application

of selective assembly system in the current body-in-white manufacturing system

of Jaguar and Land Rover company corresponding to door production. The new

technology regarding to the welding, remote laser welding, is proposed for the

door production manufacturing system. We showed that the proposed manufac-

turing system cannot provide the effective throughput as required by the company

when selective assembly system is not applied. Therefore, the application of the

selective assembly system to control part-to-part gap is shown and the benefits

of this system is provided.

Future research will be focused on the extending of the proposed analytical method for

the selective assembly systems with more quality classes. The methodological frame-

work is the same as the method applied for the two classes selective assembly system.

The attention will be focused on the integration of the proposed method into the long

transfer lines. Moreover, the analytical method could be extended to evaluate the se-

lective assembly system performance for assemblies with more than two sub-assemblies.

The proposed intelligent flow control policies to manage better the deadlock states will

be integrated into the analytical model. Finally, the method can be applied to other

manufacturing context such as battery production.

190

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