master's of science in mechanical engineering - thesis - ver 1

AN ABSTRACT OF THE THESIS OF

Bryan M. O’Halloran for the degree of Master of Science in Mechanical Engineering

presented on October 11, 2011.

Title: METHODOLOGIES TO IMPROVE RELIABILITY ENGINEERING IN

EARLY DESIGN

Abstract approved:

___________________________________________________

Robert B. Stone

___________________________________________________

Irem Y. Tumer

This thesis is the summation of two publications with the motivation to move

reliability analysis earlier in the design process. Current analyses aim to improve

reliability after components have been selected. Moving specific analyses earlier in the

design process reduces the cost to the designer. These early design analyses provide

information to the designer so that critical design changes can be made to avoid

failures. The first presents failure rates for function-flow pairs. These function-flow

failure rates are used in the Early Design Reliability Method (EDRM) to calculate

system level reliability during functional design. This methodology is compared to the

traditional reliability block diagram for three examples to show its usefulness during

early conceptual design. Next, an extension to the Function Failure Design Method

(FFDM) is presented. A more robust knowledge base using Failure Mode/Mechanism

Distributions 1997 (FMD-97) has been implemented. Then failure rates from

Nonelectric Parts Reliability Data (NPRD-95) are added to more effectively determine

the likelihood that a failure mode will occur. The proposed Functional Failure Rate

Design Method (FFRDM) uses functional inputs to offer recommendations to mitigate

failure modes that have a high likelihood of occurrence. This work uses a past

example where FFDM and Failure Modes and Effects Analysis (FMEA) are compared

to show that improvements have been made. A four step process is presented to show

how the FFRDM is used during conceptual design.

Methodologies to Improve Reliability Engineering in Early Design

byBryan M. O’Halloran

A THESIS

submitted to

Oregon State University

in partial fulfillment ofthe requirements for the

degree of

Master of Science

Presented October 11, 2011Commencement June 2012

Master of Science thesis of Bryan M. O’Halloran presented on October 11, 2011.

APPROVED:

_____________________________________________________________________

Major Professor representing, Mechanical Engineering

_____________________________________________________________________

Co-Major Professor representing, Mechanical Engineering

_____________________________________________________________________

Head of the School of Mechanical, Industrial, and Manufacturing Engineering

_____________________________________________________________________

Dean of the Graduate School

I understand that my thesis will become part of the permanent collection of Oregon

State University libraries. My signature below authorizes release of my thesis to any

reader upon request.

_____________________________________________________________________

Bryan M. O’Halloran, Author

PUBLICATION THESIS OPTION

This thesis is presented in accordance with the Manuscript Document Format option.

Two manuscripts are provided. The first was published in the 2011 International

Design Engineering Technical Conference and the second was accepted for

publication to the 2011 International Mechanical Engineering Congress and

Exposition.

ACKNOWLEDGEMENTS

I express my gratitude and appreciation to Dr. Robert Stone. His consistent support has

allowed myself to develop and has provided an optimal environment for research. I

would equally like to thank Dr. Irem Tumer for her insightful suggestions and

guidance in conducting this research. Her valuable support has steered this research to

always remain relevant. I would like to thank David Jensen for his insightful feedback.

His paper revisions were critical in the development of this research. I would like to

thank all members of the Design Engineering Lab for providing a great environment to

conduct research. Their feedback during weekly meeting had a tremendous impact on

continuing to keep this research moving forward. Last, I would like to thank Deanna

O’Halloran, my wife, Logan O’Halloran, my son, and Mike and Jennifer O’Halloran,

my parents, for their continued support for my goals. This research was funded in part

by DARPA (Subaward to FA8650-10-C-7079 with Palo Alto Research Center).

TABLE OF CONTENTS

INTRODUCTION....................................................................................................1

ABSTRACT..............................................................................................................5

INTRODUCTION....................................................................................................5

BACKGROUND......................................................................................................6

The Function Failure Design Method............................................................10

Normalized Method for Archived Data Sets Using the Heaviside Function.10

RESEARCH METHOD..........................................................................................11

Component Failure Rate Data Source............................................................11

Repository Data.............................................................................................12

Applying Rules Using the Heaviside Function.............................................14

Function-flow Failure Rates..........................................................................14

RESULTS................................................................................................................16

Proposed Methodology for Calculating System Reliability..........................16

Exploring New Functions in the Functional Model......................................17

Methodology Example Using Real Products.................................................18

CONCLUSION.......................................................................................................22

FUTURE WORK....................................................................................................23

ACKNOWLEDGEMENTS....................................................................................23

APPENDIX.............................................................................................................24

ABSTRACT............................................................................................................27

INTRODUCTION..................................................................................................27

Page

BACKGROUND....................................................................................................28

Functional Modeling......................................................................................28

Function Failure Design Method...................................................................29

Risk in Early Design......................................................................................30

Failure Rates, Modes, and Mechanisms........................................................31

Failure Modes and Effects Analysis..............................................................32

RESEARCH APPROACH......................................................................................34

Component Failure Rate Data Source...........................................................34

Failure Modes and Mechanisms Data Source...............................................35

Repository Data.............................................................................................37

Converging Data Using Matrix Multiplication..............................................38

RESULTS................................................................................................................39

Failure Mode Data.........................................................................................39

Function Failure Rate Design Method...........................................................42

Design Recommendations.............................................................................44

Failure Mode Likelihood...............................................................................46

CONCLUSION.......................................................................................................48

FUTURE WORK....................................................................................................48

ACKNOWLEDGEMENTS....................................................................................49

APPENDIX.............................................................................................................50

CONCLUSION.......................................................................................................52

VITA.......................................................................................................................55

REFERENCES.......................................................................................................56

TABLE OF CONTENTS (Continued)

Page

LIST OF FIGURES

Page

1: Series Structure of a Reliability Block Diagram....................................................8

2: Parallel Structure of a Reliability Block Diagram..................................................9

3: Function-Component Matrix................................................................................13

4: Methodology to Calculate System Reliability......................................................16

5: Reliability Results for the Electric Toothbrush....................................................19

6: Reliability Results for the Electric Bread Slicer...................................................20

7: Reliability Results for the Bottle Capping Machine.............................................21

8: Red Database Population......................................................................................30

9: Function-Component Matrix Snippet...................................................................38

10: Function-Failure Mode Matrix Snippet..............................................................40

11: Failure Mode Data for Secure Solid...................................................................41

12: Functional Model for Portable Air Compressor.................................................42

13: FFDM Step #1 Snippet.......................................................................................43



LIST OF TABLES

Page

1: Example Using Functional Basis Terminology...................................................29

2: FFDM Example for a Portable Air Compressor..................................................45

3: Additional Recommendations for the Portable Air Compressor.........................46

4: Failure Rates of Failure Modes for Portable Air Compressor.............................47

LIST OF DEFINITIONS

Failure: Undesirable loss in functionality during a specified life

Failure mode: Observable consequence of a failure or change in behavior from a failure

Failure mechanism: Physical process which causes a failure

Function: What the system does to accomplish a task

Component: Solution to a function which has physical form

Occurrence: A single data point based on a relationship

Design Repository: Database of product information and design tools

Constant failure rate: Number of failure of the design divided by the operation time of the design

Failure Probability:Probability that a failure will occur under the stated assumptions of the analysis

METHODOLOGIES TO IMPROVE RELIABILITY ENGINEERING IN EARLY

DESIGN

INTRODUCTION The field of Reliability Engineering is concerned with managing, studying,

evaluating, and mitigating failures in design and manufacturing. Using reliability

engineering analyses in design can improve availability, reduce maintenance and cost,

and improve safety for the customer. In general, reliability of a design is viewed

separate from functionality and requires independent analyses. These analyses exist

mostly for the later stage of design, once a computer model or physical prototype has

been developed. There are many reasons why this is true, for example failure

occurrence data is recorded for failed components, not lost functionality. It is also

impossible to evaluate properties such as stress for functionality; however, this is

common practice for components. The early stages of design lack formal methods in

reliability engineering. This research produces a means to address this need.

Traditional reliability engineering analyses have been used to increase safety

and reduce the likelihood of failures for many years. As the field of reliability

engineering grows, so do the efforts to increase its presence in early design. This

research has focused on moving reliability analyses into the functional design stage.

Functionality is the stage where the voice of the customer is captured to describe what

the product must do. For this reason, failure can be defined as the loss of functionality

[1]. When a design stops working the way a customer prefers, it has failed. Since we

design for functionality, methodologies in this research has been formulated to provide

designers the capability to perform reliability analyses directly after generating a

functional model. Functional modeling is performed at the conceptual stage of design

before any components have been selected [2].

There are a variety of reasons to increase the presence of reliability

engineering in early design. One reason is that offers the designer cost-effective

choices. Later in the design process choices become increasingly expensive and

complicated to implement. The goal of this research is to provide the designer with

1

more knowledge from which these important decisions can be made. Knowledge, in

the form of methodologies, guides the design toward a more reliability solution. Each

of the two methodologies presented here uniquely contribute during the design

process.

In the first manuscript a methodology is developed to calculate function-flow

failure rates using component failure rates. This process uses the Design Repository

for function to component mapping, a Heaviside function to eliminate noise in the

data, and simple computations and logic statements to arrive at the function-flow

failure rates. The result is a minimum, maximum, and weighted average function-flow

failure rate. This process can be reproduced using different components, component

failure rates, functional languages, occurrence data, or Heaviside rules. Similar to

component failure rates, this data can be used to select reliable function-flows during

the design process, or can be employed in traditional reliability engineering analyses

such as Functional Reliability Block Diagram (FRBD). A methodology is presented to

calculate system level reliability using an FRBD style approach. Within this

methodology, the step mitigate failure rates is used as a design tool to increase the

reliability.

In the second manuscript, improvements are made to an existing methodology,

namely the Function Failure Design Method (FFDM) [3]. New data is added to

determine a relationship between functions and failure modes is increased and an

additional step is added to convert occurrence data to rate data. Within this process,

the Design Repository was used to acquire the link between functions and

components. Failure Mode/Mechanism Distribution (FMD-97) [4], a comprehensive

manual from the Reliability Information Analysis Center (RIAC), was used to

generate a matrix linking components to failure modes. Component failure rates are

used to convert occurrence data to rate data. This allows the failure modes to be

prioritized by the likelihood of occurrence. The rate data in the function to failure

mode matrix was calculated to be used in the Function Failure Rate Design Method

(FFRDM), however the process to calculate the data can be redone using different

initial data.

2

Also in the second manuscript, FFRDM is presented to provide critical failure

information in the conceptual design stage to reduce the likelihood of failure. This

data shows the designer the likelihood that a function-flow will fail in a specific failure

mode. FFRDM is shown to expand on the Function Failure Design Method (FFDM) to

prioritize failure modes, making the decision on which failure mode to mitigate. A

significant amount of data has been added to expand the knowledge base to provide

more robust results. FFRDM was tested on the design of a portable air compressor to

show improvements in prioritizing the failure modes. This was a previous example

where FFDM was compared to failure modes and effects analysis (FMEA). It is

shown that improvements in FFDM have been accomplished by determining

additional failure modes which were overlooked in the original comparison.

In this research FFRDM is discussed as an alternative to FMEA. However, it

should also be noted that FFRDM can supplement a portion of FMEA. For new

designs, FMEA generally requires guessing failure modes. FFRDM can first provide a

list of failure modes for new designs based on historical data. Second, it can accurately

quantify the probability of occurrence. The output of FFRDM should to be converted

to a 1 - 10 scale for compatibility with FMEA.

Performing reliability analysis at the conceptual level of design offers the power

of risk informed decision making to the designer. As the design process continues it

becomes increasingly expensive to make design changes. Providing an analysis that

can mitigate this problem at the conceptual level may significantly reduce the

likelihood of costly failure events.

3

Early Design Stage Reliability Analysis Using Function-flow Failure Rates

Authors

Bryan M. O’Halloran

100 Dearborn Hall

Email: [email protected]

Robert B. Stone Ph.D

406 Rogers Hall


Irem Y. Tumer Ph.D

408 Rogers Hall


Proceedings of the ASME 2011 International Design Engineering Technical

Conferences

Design Theory and Methodology Conference

IDETC/CIE 2011

August 28-31, 2011, Washington D.C., United States of America

4

mailto:[email protected]






ABSTRACT

In this paper, failure rates for function-flow pairs are presented. This data creates an

opportunity for the designer to move reliability analysis earlier in the design process.

The function-flow failure rates can be used to make design decisions before

components are selected giving the designer increased knowledge to explore

alternative options. A reliability block diagram approach has been adopted to evaluate

the reliability of three designs at both the functional and component level. The results

show that the bounds from the functional reliability overlap those of the component

reliability.

1. INTRODUCTION

Traditional reliability engineering techniques have been used to increase safety

and reduce the likelihood of failures for many years. As the field of reliability

engineering grows, so do the efforts to increase its presence in early design. The early

design phase has the distinct advantage of offering the designer cost-effective choices

as opposed to later in the design process. The premise of this research is to provide the

designer with more knowledge to which these important decisions can be made. Data,

which can be used in a variety of ways, is presented here in the form of function-flow

failure rates. Similar to component failure rates, this data can be used to select reliable

function-flows, or can be employed in traditional reliability engineering analyses such

as Functional Reliability Block Diagram (FRBD). Specifically, a methodology was

proposed to calculate the system level reliability using FRBD and function swapping

to show the usefulness of the data.

The scope of this research is to first present minimum, maximum, and

weighted average function-flow failure rates. This information is based on collected

data and is not intended to demonstrate failure modes or mechanisms. Second, a

design methodology is introduced to calculate system level reliability at the functional

level.

5

2. BACKGROUND

This section provides a survey of related research including several traditional

and non-traditional reliability engineering techniques, FFDM, and the use of a

normalization method to account for variations in archived data sets.

Traditional risk and reliability analysis techniques exist primarily to move failure

assessments into the earlier stages of design. These efforts look at system components,

critical events, and system characteristics to assess risk and reliability during the

design phase. Reliability engineering techniques can help engineers better meet the

needs of customers. In general, customers want two things out of a product. First they

want the product to function properly according to their needs, and second they want it

to function reliably. Assessing reliability during the design stage helps drive designs to

function reliably. In reliability engineering failure is defined as a design not

functioning as originally intended for a given life in specific operating conditions [1].

There are several methods used to increase the reliability of the design including

Failure Modes Effects and Criticality Analysis (FMECA), Event Tree Analysis (ETA),

Fault Tree Analysis (FTA), and Reliability Block Diagrams (RBD). Each of these

analyses accomplishes a different goal and are each used during the design process.

The goal of FMECA is to identify, evaluate, and prevent critical component

failures [5]. Critical components are determined by the risk priority number (RPN).

Components with high RPN values receive a recommended action and schedule to

resolve their being critical. The FMECA analysis starts by identifying a list of

components and their potential failure modes. The RPN value is the product of three

variables; occurrence, severity, and likelihood of detection. Occurrence refers to the

likelihood that the failure will occur, severity is how bad the failure is, and likelihood

of detection is how hard it will be to detect. From the list of potential failures, the

occurrence, severity, and likelihood of detection are scored on a scale of 1 to 10,

resulting in an RPN value of 0 to 1000. The usefulness of FMECA as a design tool is

to look at the RPN values relative to each other and determine which components

6

needs action taken and which do not. From this analysis, the designer can determine

the critical components of a system and make design changes accordingly.

A variety of software tools and methodologies exist to improve and automate

FMEA including FMEA streamlining [6], WIFA [7], FLAME [8, 9], CFMA [10], and

Advanced FMEA (AFMEA) [11, 12]. Although, these automated tools are not capable

of predicting failures.

ETA is a bottom-up approach to system reliability analysis and is used to

determine the likelihood of an outcome based on an accidental event [13]. This shows

the designer end failure states that have a high probability of occurring. ETA uses the

probability of different failures occurring in the system combined with the probability

of safety barriers to determine the final state probabilities. A safety barrier is anything

in the design used to resolve a failure in the chance that is occurs. This would, for

example, be a ceiling sprinkler system in the event of a building fire. ETA is

computationally simple to perform, although depending on the number of accidents

analyzed and the level of detail explored, it can be lengthy. The usefulness of this

method is in the ability to determine accurate probabilities for events and barriers, then

make design decisions to increase the system reliability. It can be difficult to

accurately define the probabilities of events and barriers [14]. Design decisions cannot

be made with confidence unless these probabilities are well accepted. A fuzzy logic

has been developed to account for this. Specifically it determines the uncertainty in the

probability of failures and defines a qualitative impact of certain outcomes. This also

can be a useful tool for decision making.

FTA is a top-down approach to reliability analysis which begins with an

undesirable state and determines the initial cause [15]. Events that could cause the

undesirable event are listed in the row below it. Beneath each of the row 1 events are

row 2 events. This continues until a basic event is reached where there does not exist a

further occurrence to cause it. Between each row are the connections and logic gates

that define each of the relationships. In general, two types of logic gates are used;

“AND” and “OR”. AND gates require that each of the events in the next row must

occur for the event to occur. OR gates only require a single event in the next row to

7

occur for the higher level event to occur. Probabilities are assigned to each event so

the probability of the top failure event can be determined. The top event probability is

simple to calculate. In order to perform FTA, the system must be well understood so

everything is captured.

RBD are another method used to determine system level reliability of a design

during the design stage [16]. This is useful when requirements dictate the level of

reliability a design can have. For complex systems, these diagrams are useful as a

visual tool to see where failures will occur. They also make computation simple to

perform. Although, the diagram itself is not used to show the architecture of the

system, but instead only to provide graphical information on how it fails. Meaning that

if components are connected in the RBD, this does not necessarily mean they are in

the physical design. In general, there are two structure types; series and parallel. These

refer to the a theoretical path of working components that a design can take to

accomplish its overall function. If the structure is series, there is only a single path and

all components along that path must function properly or the design fails.

FIGURE 1: Series Structure of a Reliability Block Diagram

If the path splits into a parallel structure, any path is sufficient to accomplish

the function. In other words, there must always exist a path from start to finish of

properly functioning components in order for the design to be functioning. For

example, two motors running in parallel to drive the same component where either

motor meets the power requirement for the overall system. The system can still

function if one of the motors fails.

C1 C2 C3

8

FIGURE 2: Parallel Structure of a Reliability Block Diagram

Failure rate data for each component, given by the variable (λ), is needed to

calculate the reliability. Also, a time value (t) is needed since reliability is time

dependent. For electromechanical designs with constant failure rates it can be assumed

that the reliability behaves according to an exponential distribution. Equations (1-3)

calculate the system level reliability using an exponential distribution assuming

failures are independent.

These are useful to determine the system level reliability to meet design

criteria. The designer can also use the RBD to add redundancies that increase

reliability. Problematic areas become easy to identify in a large design using this

technique.

A disadvantage to generating RBD is the high user workload. A variety of

software tools have automated this process including Reliasoft BlockSim – Version

C1

C2

C3

!!"#$"! ! !!!!!! (1)

!!"#"$$%$ ! !! !! !!!

!!! (2) !! ! !!!!!! (3)

9

6.5.2, ARINC Raptor – Version 7.0.07, and Relex Software Reliability Block Diagram

[17].

Less common methods such as Synergetic Reliability Prediction (SYRP) are

also used during the design process to predict later life failure [18]. This method has

been shown to be accurate but requires an in-depth and lengthy analysis and expert

knowledge to perform. Work has been done to estimate the probabilities of failures

using the mean time between failure, but is a lengthy process and requires a significant

amount of work to understand [19].

2.1. Function Failure Design Methodology

FFDM is a structured formulation of the function-failure analysis method

introduced by Tumer and Stone, and is used to perform failure analysis in the

conceptual design stage [20]. This method also aids the designer by using a function-

based concept generator approach which helps streamline the design process. FFDM is

a start-to-finish design method which utilizes knowledge bases that link product

function to failure modes and product function to design concepts. The knowledge

base data is archived in the form of a function component matrix and reduces the need

for the designer to have a large intellectual knowledge base.

FFDM has several advantages over other reliability engineering methods

including reduced high user workload, using archived failure knowledge base, being

usable during functional design, using a formalized failure language, and is practical

for electrical and mechanical systems [21]. However, FFDM lacks a strong component

to failure mode relationship, limiting the usefulness of the results.

2.2. Normalization Method for Archived Data Sets Using the Heaviside

Function

An archived set of product data inevitably contains a certain amount of

variations. This would, for example, include data completeness and correctness.

Normalization methods provide a systematic way to lessen the impact of data

variations.

10

McAdams and Wood used a norming method to develop a quantitative design-

by-analogy metric based on the functional similarity of products [22]. This norming

method uses a pair of rules to account for differing product customer needs importance

and complexity. Data was represented using a product function matrix for easy

manipulation and data structuring. Each matrix element is the product of 2 ratios; the

number of functions in a particular product over the average number of functions in a

product and the average customer needs rating over the customer needs for a particular

product. Norming this data gives the designer a way to calculate the similarity metric

of a design. This value is then used to select analogous designs.

The Heaviside function is used as a conditional binary multiplication see

equation 4. In the case that a specific cell value is equal, or not equal, to zero the value

of the Heaviside becomes one, or zero. To determine the average number of functions

for a product the Heaviside function was summed across each row and column.

(4)

3. RESEARCH APPROACH

This section presents the method for determining the function-flow failure

rates. The steps include finding component failure rates, mapping functions to

components, validating the data, and calculating the minimum, maximum, and

weighted average function-flow failure rates.

3.1. Component Failure Rate Data Source

Nonelectric Parts Reliability Data (NPRD-95) [23] was used as the source of

the component failure rate data. This reference is an ongoing effort to collect and

provide high volumes of data from a variety of sources including both military and

commercial. This specifically includes warranty manuals, government sponsored

studies, published papers and reports, databases, and military maintenance systems.

11

The number of functions in the j th product is

! j!"i!1

m

H#$ i j%. (4)

The average number of functions is

!̄!1

n "i!1

m

"j!1

n

H#$ i j%. (5)

H is a Heaviside function defined as

H#x %!! 1 when x&0

0 when x!0. (6)

In the above equations, n is the number of products, and m is thetotal number of different functions for all products.Figure 2 shows the complete normalization process for some

hypothetical set of products. The top left matrix in the figure #a% isthe original matrix '. Moving from left to right and then down inthe figure, first the matrix is adjusted to equalize product impor-tance #b%. This is done be multiplying $ i j by the scaling coeffi-cient ((̄/( j) as computed from '. Then this term is multiplied bythe scaling coefficient (! j /!̄) as determined from the matrixshown in #c%. The result is the final matrix N shown in #d%. Thefunctions in the N matrix are comparable for importance fromproduct to product.

3.3 Computing Similarity. The elegance and power of thisvector representation are made clear in the development of thequantified product similarity metric. Using the matrix representa-tion, N, the entire domain of products can be reviewed for func-tional similarity. The product vectors generated from Eq. #1% arerenormalized so that their norm is 1. After scaling, the inner prod-uct of the normalized product vectors for each combination ofproducts is calculated. Forming the inner product between a prod-uct a and a product b, a!b , gives the projection of product a onproduct b. Forming the inner product of a product with itself #thecompletely similar product% gives a value of 1. Forming the innerproduct of a product with one that shares no common functionsyields a result of zero. If the product vectors had not been renor-malized to unity, it would be possible to have a product moresimilar to another product than itself. Such a potential result isremoved by the renormalization.

Once calculated, this projection is a product similarity metric.This projection is denoted with a )ab and is defined as the innerproduct between the product vectors for products a and b. Themeasure ) is based on the number of common functions in bothproducts and the customer importance of those functions. In otherwords, this projection provides the desired measure of productsimilarity. It is a simultaneous measure of functional similarityand customer importance. A graphical representation of this pro-jection is shown in Fig. 3. In this figure a portion of the functionspace is shown for the functions secure solid, convert electricity torotation, and position solid. Product vectors for Product A andProduct B and the projection of Product B on Product A areshown. This represents the similarity metric )BA for these twoproducts.For clarification of the formulation of ) consider the following

representative numerical example. Shown in Table 3 are the prod-uct vectors for Product A and Product B. Forming )BA

gives (0.22,0.44,0.87)!(0.54,0.71,0.54)!0.22"0.54#0.44"0.71#0.87"0.54!0.55A matrix of these projections is

*!NTN. (7)

N is the matrix of unity-normalized product vectors, similar to N.Each element, ) i j , is the projection of the ith product on the j thproduct. * is the product similarity matrix. Using matrix multipli-cation to form the product similarity matrix * is similar to atechnique Taylor +15, used to determine topics and frequencies ofdiscussion on internet newsgroup communication in student de-sign teams. The product projections with high ) values are candi-dates for finding meaningful design by analogy information at thefunctional level.As this similarity metric is computed in real time, the only data

that need to be stored and accessed to allow for broad applicationof this method are customer need weighted functional models.This approach greatly reduces the overhead in data storage neededfor locating similar products. The fundamental work needed toallow the generation of data to be performed by any designer iscurrently in progress +16,.

Fig. 2 Normalization process: „a… original function-productmatrix !, „b… equalizing product importance, „c… determiningaverage number of functions per product, and „d… scaling forproduct complexity to get the final matrix N

Fig. 3 A graphical interpretation of the product functionalsimilarity projection

Table 3 Product vectors for Products A and B.

Product A Product B

convert electricity to rotation 0.54 0.22position solid 0.71 0.44secure solid 0.45 0.87

176 Õ Vol. 124, JUNE 2002 Transactions of the ASME

Downloaded 26 Jan 2010 to 165.91.149.125. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

! ! = {1 !ℎ!" ! ≥ !}{0 !ℎ!" ! < !}

From the previous publication, NPRD-91, 56% more data has been acquired. A strong

emphasis was put on data quality during the collection phase. This was done by

ensuring completeness of data, consistency of data, equipment population tracking,

failure verification, and characterization of operation histories. Often data is discarded

if it does not meet quality standards. Also, this document did not indicate failure

modes or mechanisms. Failure, as observed in NPRD-95, is classified generically

under solving the symptoms of the failure. A part failed if, when it was replaced, the

failure symptoms were not present anymore.

Comprehensive indices are provided for background on the parts and sampling.

These include the component manufacturer, model or part number, nominal

performance specifications specific to each part, population tested, number of

operation hours, and number failed. The operating hours and number of parts failed is

used to generate failure rates for both specific components and component classes. For

example, a failure rate is provided for a specific type of actuator, then a combined

failure rate is given for the actuator class. The failure rate for each component class is

the sum of the total components failed for that class divided by the sum of the

operating hours for each component in that class. Calculating both types of data lets

the user employ the data at a generic or specific level.

3.2. Repository Data

The Design Engineering Lab Repository (http://designengineeringlab.org/

delabsite/repository.html) at Oregon State University was used for function component

mapping and data structuring. A tool within the repository has the capability to

generate Microsoft Excel spreadsheets based on the designer’s intent. For the purpose

of this research, a function-component matrix (FCM) was created with function-flows

and using the component naming.

The FCM is used to capture the relationship between the functions and

component naming terms. Structurally, the FCM lists component naming terms across

the first row as column headers and function-flow pairs down the first column as row

headers. Elements of the matrix are then filled with the occurrences of the number of

12

http://designengineeringlab.org/delabsite/repository.html




times a function is solved by a component. Initially there are 164 components listed

and 731 function-flows. The total number of occurrences is 16,365.

FIGURE 3: Function-Component Matrix

The example FCM snippet in Figure 3 shows convert rotational to

translational being solved twice by the coupler. Zeros in the matrix indicate that there

is no observed relationship in the repository of the particular function-flow and

component.

The component naming terms along the first row of the FCM are specifically

defined [24]. These terms line up with the component classes listed in NPRD-95. The

data was translated over from NPRD-95 and entered into the Excel spreadsheet. For

names that did not match identically, the component naming definitions were used to

justify that the data was correctly being transferred. For components without data, an

X was entered for the component failure rate.

Function(Component-MatrixFailures/Mhours 192.0795 x 0.1949 2.2727 15.4501 0.1624 x xGenerated-On:-Wed-Jan-26-22:44:46-PST-2011 converter conveyer coupler cover crank digital-display diode distributorconvert-pneumatic-to-status 0 0 0 0 0 0 0 1convert-pneumatic-to-translational 0 0 0 0 1 0 0 0convert-radioactive/nuclear-to-chemical 0 0 0 0 0 0 0 0convert-radioactive/nuclear-to-control 0 0 0 0 0 0 0 0convert-radioactive/nuclear-to-electrical 0 0 0 0 0 0 0 0convert-rotational-to-acoustic 0 0 0 0 0 0 0 0convert-rotational-to-electrical 0 0 0 0 0 0 0 0convert-rotational-to-hydraulic 0 0 0 0 0 0 0 0convert-rotational-to-mechanical 0 0 0 0 0 0 0 0convert-rotational-to-pneumatic 0 0 0 0 0 0 0 0convert-rotational 0 0 0 0 0 0 0 0convert-rotational-to-status 0 0 0 1 0 0 0 0convert-rotational-to-translational 0 0 2 0 0 0 0 0convert-signal-to-status 0 0 0 0 0 0 0 0convert-signal-to-visual 0 0 0 0 0 1 0 0convert-solar-to-chemical 0 0 0 0 0 0 0 0convert-solar-to-electrical 2 0 0 0 0 0 0 0convert-solar-to-status 0 0 0 0 0 0 0 0convert-solar-to-thermal 1 0 0 0 0 0 0 0convert-solid-to-chemical 0 0 0 0 0 0 0 0convert-solid-to-liquid 0 0 0 0 0 0 0 0convert-solid 1 0 0 0 0 0 0 0convert-solid-to-solid(solid 0 0 0 0 0 0 0 0convert-status-to-analog 0 0 0 0 0 0 0 0convert-status-to-control 0 0 0 1 0 0 0 0convert-status-to-electrical 0 0 0 0 0 0 0 0

13

3.3. Applying Rules Using the Heaviside Function

As a means to take the failure rate listed for a specific component to individual

function-flows, it is important to avoid letting particular components dominate the

data. For example, a nozzle has solved couple solid three times out of 2045. Since the

nozzle has a high failure rate of (718 failure per million hours), couple solid will also

have a high failure rate. However, the nozzle solves the function couple solid in this

particular case, it is an exception rarely observed. The Heaviside function has been

used as a way to assign an importance rating. The occurrence data must meet the

requirements of the Heaviside function according to the following rules.

Rule 1: A function-flow must be solved at least 3 times.

This requires that any function will either see a variety of failure data because

it is solved by different components, or has been solved by the same component at

least three times.

Rule 2: A cell must contain greater than 1% of the total occurrences for the entire

component.

For a component that has 100 occurrences, a function-flow must be solved

more than once by this component or the failure rate is not inherited. This rule will

eliminate function-flows from inheriting failure rates when their solution is an

exception to how the component is generally solved.

3.4. Function-flow Failure Rates

The process to use the data to determine the functional failure rates after

applying the rules is described here. The process to determine the weighted average

differs from that of the minimum and maximum and is described in the following

paragraph.

14

The matrix resulting from the Heaviside calculation, named T2, was used as a

starting point to determine the weighted average failure rate. Another matrix was

formulated to prepare for the final calculations which used a logic test to determine if a

cell has an occurrence greater than zero, then if that particular component had failure

rate data. These preparation steps avoid mathematical and programming errors such as

adding up X’s or dividing by zero. The following line of code tests is a cell contains an

X, if the sum of a row is greater than zero, if a component failure rate is greater than

zero, and if the failure rate is listed as X.

=IF('T2'!B31>0,IF('T2'!$FK31>0,IF('FCM (Mhours) 2'!E$4>0,IF('FCM (Mhours) 2'!

E$4="x","x",('T2'!B31*'FCM (Mhours) 2'!E$4)),"x"),"x"),"x")

When the final statement is false and the first three are true, the component failure rate

is multiplied by the occurrence. These values, across a row for a specific function-

flow, were summed and divided by the total number of occurrence for the same

function-flow. The following line of code completes the calculation for the weighted

average function-flow failure rate.

=IF(SUM('T3'!B35:FI35)>0,SUM('T3'!B35:FI35)/'T2 (2)'!$FK35,"x")

The total occurrences were those that occurred when the component also had failure

data. This way, components that were not counted in the summation were also not

counted in the total number of occurrences. This calculation determined the weighted

average function-flow failure rates.

To determine the minimum and maximum failure rates, the matrix T2 was

converted into a binary matrix containing values of only 1 and 0. A binary matrix is

used only to show that there exists a relationship between a function-flow and a

component. This eliminates the occurrence information since it does not capture the

one to many relationship between function-flow and component. This is due to how

the FCM is constructed. A component is listed, then the occurrences for it solving each

15

function-flow are listed in the same column. This data represents only when one or

more functions are solved by the same component. It does not reflect the occurrences

when a single function is solved by multiple components. In this instance, each

component that solves a part of this function-flow would list a value of 1 for that

function-flow in its own column. This results in the solution for that function-flow

adding up to greater than one.

4. RESULTS

This section presents the results of the function-flow failure rates. This data is

presented in a complete table in Appendix A. An RBD style failure analysis has been

adopted for validation. Both RBD’s and the proposed methodology are used to

calculate system level reliability of each design to evaluate the usefulness of the

calculated data. This comparison is done using three different designs.

4.1. Proposed Methodology for Calculating System Reliability

This process involves five steps. Figure 4 provides an overview and flowchart

for the proposed methodology.

This analysis begins by generating a complete functional model. All functions

and flows necessary to satisfy the customer needs must be present. Function-flows are

then restructured to reflect the FRBD instead of the functional model. Each function-

flow is placed in a box, then the designer must reason about its role in the overall

system failure. If the function-flow fails, will the entire design fail, or is there an

additional functionality that would keep this from occurring? In the case where there is

not, this function-flow is in series in the FRBD. If there is additional functionality,

these two function-flows are in parallel. Next, data is pulled out of Appendix A for

each function-flow. All values including minimum, weighted average, and maximum

should be recorded. Functionality can be added or functions can be swapped to reduce

the combined failure rate. This is explained in section 4.2. Equations (1-3) are then

used to calculate the reliability in the same manner as a traditional RBD. This should

16

be individually calculated for the minimum, weighted average, and maximum failure

rate.

Generate Functional Model

Reformat Using Reliability Block Diagram Structure

Gather Failure Rate Data

Mitigate Failure Rates

Perform Reliability Block Diagram Calculations

FIGURE 4: Methodology to Calculate System Reliability

4.2. Exploring New Functions in the Functional Model

Exploring functions to reduce the combined failure rate using this framework

is done one of two ways. First, functions can be swapped out for new functions which

have lower failure rates and second functions can be added using a parallel structure in

the RBD.

This data can be used to let the designer know when to explore different

functions in the functional model. Certain function-flows with high failure rates can be

exchanged with others to generate alternate final designs. This leads to a component

with a low failure rate solving the function-flow. Since functional modeling is

performed at an abstract level and problem statements are often not well defined, new

functions can be explored in place of others to solve the same blackbox function.

Another option when the basic functionality is strictly required by the product is to

add mitigating functions for the high failure rate functions. For example, if the

17

function convert pneumatic energy to mechanical energy has an unacceptable failure

rate and is known to historically fail from overheating, additional functionality to

mitigate this failure can be used. This could be distribute thermal energy or export

thermal energy. In the RBD this would reduce the final failure rate because the new

functionality would be in parallel with convert pneumatic energy to mechanical

energy. In reality, this would be adding a heat sink which is commonly done to relieve

heat from a system and reduce the likelihood of failure.

4.3. Methodology Example Using Real Products

As a way to validate the proposed methodology using the function-flow failure

rates, examples have been provided. Three products each with functional models (FM)

and configuration flow graphs (CFG) were found [22, 25]. An RBD approach has been

adopted to measure the reliability of each CFG. These traditional RBD were

constructed with component failure rates from NPRD-95. In the reliability calculation

an exponential distribution of failure rates was assumed. Since products have

relatively few components and no redundancies, it was determined that the RBD

structure was entirely in series. That is, if any component fails, the overall function is

no longer accomplished.

In order to use the functional failure rates, the proposed methodology is used.

Again, the three products are relatively simple and do not contain any parallel

structures or redundancies. For more complex systems, redundancies would be present

in the RBD structure resulting in a combination of parallel and series structures.

The three products evaluated were an electric toothbrush, an electric bread

slicer, and an automated bottle capping machine. Each product had an overall

reliability calculated from the traditional RBD, and for comparison purposes a

minimum, maximum, and weighted average reliability using the proposed

methodology. Time values were selected to reflect a reasonable operation for each.

The first product explored was an electric toothbrush. The blackbox function of

this product is to separate solids. The results in Figure 5 show that the average

reliability at 1,000 hours is 95%. The proposed methodology results were compared

18

relative to the traditional RBD. The maximum is less than 1% higher while the

minimum is significantly lower, only 7% reliable at 1,000 hours. The weighted

average is 4% lower. This result is expected based on the components and function-

flow pairs present in the design. The largest component failure rate seen in the product

was the link with a value of 10.97 failures per million hours and the lowest was the

housing at 0.013 failures per million hours. The function with the greatest failure rate

was export solid with a value of 717 failures per million hours. The minimum was

found in the function-flow import solid at 0.0018 failures per million hours.

FIGURE 5: Reliability Results for the Electric Toothbrush

Four function-flows and two components were not included in the reliability

calculations. These components included electric wire and guiders. Electric wire does

not have failure rate data in NPRD-95. The rate for guiders was excluded because the

function-flows that it maps to does not have data. These function-flows include

convert rotational to translational mechanical energy and transfer translational

mechanical energy. Similarly, transfer electrical energy was excluded as a result of the

missing electrical wire data. Mix solid to mixture did not receive failure rate data as a

result of not passing the rules discussed previously. This is one of many functions

accomplished by the brush component on the toothbrush. The brush was left in the

calculation as were the other function-flows that is solves.

95.1%& 95.9%& 91.1%&

19.5%&

CFG& Maximum& Average& Minimum&

Electric(Toothbrush(Reliability&

19

The next product tested was an electric bread slicer. This product also

separates solids, but uses a different variety of components to accomplish its blackbox

function. The reliability found from the RBD at 1,000 hours was 96%. The results

from the proposed methodology show the minimum, maximum, and weighted average

were found to be 85%, 99%, and 96% respectively. The results for this product show a

strong correlation between the traditional RBD and the weighted average from the

proposed methodology. Components in the electric bread slicer with the highest and

lowest failure rates were the handle (11.01 failures per million hours) and an electric

switch (0.82 failures per million hours). For the function-flows these were both import

human energy and actuate electrical energy (25.81 failures per million hours) and

import electrical energy (0.0021 failures per million hours).

FIGURE 6: Reliability Results for the Electric Bread Slicer

Two components and five function-flows were not included in the reliability

calculations. Both blade and electric wire are without failure rate data in NPRD-95

and therefore their corresponding function-flows were not included in the calculation.

These function-flows include transfer electrical energy, import solid, secure solid,

separate solid, and export solid.

The third product tested was an automated bottle capping machine. This

product imports a bottle on a belt, grabs it with a clamp, caps it, then exports the

96.2%&98.7%&

96.5%&

85.0%&

CFG& Maximum& Average& Minimum&

Bread&Slicer&Reliability&

20

capped bottle. The blackbox function of this product is to couple solids. The reliability

of the bottle capping machine at 10,000 hours was 61%. The results from the proposed

methodology for the minimum, maximum, and weighted average were found to be

7%, 76%, and 49% respectively. The components with the highest and lower failure

rates were a handle (11.01 failures per million hours) and an electric conductor (0.019

failures per million hours). Function-flows with the highest and lowest failure rates

were both actuate electrical energy and import human energy (25.81 failures per

million hours) and import electrical energy (0.0021 failures per million hours).

FIGURE 7: Reliability Results for the Bottle Capping Machine

Eleven components and twelve functions were excluded from the reliability

calculations. This was due to either the function-flow or component not having failure

rate data. In either case, the components and function-flows were mapped to each

other and both were excluded.

Without being able to account for the data in a design, uncertainty is

introduced to the calculation. This is a limitation to the choice of using the function-

flow failure rates in the proposed methodology. The three products evaluated were not

chosen because they had failure rate data, as this would not be the case in a design

project. They were chosen because they had complete CFG and FM which were

already generated.

61.1%%

76.1%%

48.8%%

7.1%%

CFG% Maximum% Average% Minimum%

Bo#le&Capping&Machine&Reliability%

21

In the three designs evaluated, two function-flows resulted in two components

that ultimately lowered the system level reliability. These functions include export

solid, and converts electrical energy to rotational mechanical energy, and their

corresponding components were brush, and electric motor.

In the toothbrush, the two brush components had a combined series failure rate

of 18.30 failures per million hours while their corresponding function-flows had a

combined failure rate of 56.92 failures per million hours. The brushes individually had

the second highest failure rate in the product and account for approximately half of the

failures that would occur in the toothbrush. Similarly, their corresponding function-

flows make up for half of the failures in the weighted average.

For the automated bottle capping machine, the component with the highest

failure rate, an electric motor, was present twice in the design. The combined series

failure rate of these motors is 18.48 failures per million hours. In this design, the

electric motor converts electric energy to rotational mechanical energy. This function

occurs twice in the functional model and has a combined failure rate of 18.77 failures

per million hours. The two electric motors account for approximately 40% of the

overall failure rate while the conversion from electrical to rotational energy accounts

for approximately 25% of the combined failure rate using the proposed methodology.

This information shows that critical components can be identified using the

proposed methodology. The comparison between these shows a positive result for the

use of the proposed data. Understanding the range for the reliability before any

components have been selected is a useful tool in the early design stage.

5. CONCLUSION

The effort to move reliability engineering into the early stage of design is an

increasing area of interest. This research aims to increase knowledge of the system at

the functional level.

Currently, failure rate data is available for components. Here similar data has

been generated for function-flows to give designers the same advantage at the

functional level of design. This was done using a FCM and the Heaviside function.

22

The Heaviside function required that function-flows were solved with enough

occurrences to be counted which protects them from inheriting failure rate data from

components that are rarely their solution.

The new failure rate data has been used to make decisions at the design phase

and determine system reliability with a weighted average and an upper and lower

bound. This was done using the proposed methodology.

6. FUTURE WORK

The component failure rate data used from NPRD-95 does not give any

indication of how a component failed. As discussed previously, a failure observed in

this document was described as solving the symptoms of failure. Research has been

done to break function failures into failure modes based on a set number of failures.

This method will be examined to find a way to get a failure rate of a failure mode for a

specific function-flow. This data provides the designer more information in the early

design stage and will help guide important design decisions

7. ACKNOWLEDGMENTS

This research was funded in part by DARPA (Subaward to FA8650-10-C-7079

with Palo Alto Research Center). The opinions, findings, conclusions, and

recommendations expressed are those of the authors and do not necessarily reflect the

views of the sponsors.

23

APPENDIX A: Function-flow Failure Rates

Function-flow Wtd Avg Min Max Function-flow Wtd Avg Min Max

Fails/Mhours Fails/Mhours Fails/Mhours Fails/Mhours Fails/Mhours Fails/Mhours

actuate control 1.97E+0 8.20E-1 2.58E+1 display status 5.40E+1 5.40E+1 5.40E+1actuate control to electrical 8.20E-1 8.20E-1 8.20E-1 distribute electrical 4.30E+0 5.28E-1 8.08E+0actuate electrical 1.25E+0 1.79E-1 2.58E+1 distribute liquid 2.41E+2 2.92E+0 7.18E+2actuate human energy 1.79E-1 1.79E-1 1.79E-1 distribute material 3.64E+2 9.15E+0 7.18E+2actuate human material 1.79E-1 1.79E-1 1.79E-1 distribute mechanical 8.89E+0 1.95E-1 2.08E+1actuate mechanical 7.25E+0 1.79E-1 2.58E+1 distribute optical 5.73E-1 5.73E-1 5.73E-1actuate solid-liquid 5.84E+0 5.47E+0 6.20E+0 distribute solid 7.18E+2 7.18E+2 7.18E+2change control 4.59E+0 4.59E+0 4.59E+0 distribute thermal 6.43E+0 6.12E-2 1.97E+1change electrical 2.01E+0 9.00E-2 4.59E+0 export acoustic 6.63E+0 6.63E+0 6.63E+0change electromagnetic 7.48E+0 2.21E-2 1.12E+1 export control 2.10E-3 2.10E-3 2.10E-3change hydraulic 3.93E-1 3.93E-1 3.93E-1 export electrical 1.84E+0 1.90E-2 3.61E+0change liquid 7.18E+2 7.18E+2 7.18E+2 export electromagnetic 2.27E+1 5.73E-1 4.48E+1change material 1.23E+2 5.40E+1 1.92E+2 export gas 1.17E+2 2.25E+0 7.18E+2change mechanical 5.11E+0 9.30E-1 1.97E+1 export human energy 1.79E-1 1.79E-1 1.79E-1change rotational 4.56E+0 2.92E+0 4.69E+0 export human material 3.12E+0 1.31E-2 1.97E+1change signal 1.92E+2 1.92E+2 1.92E+2 export hydraulic 6.84E+0 1.95E-1 1.34E+1change solid 1.45E+2 2.00E-2 7.18E+2 export liquid 2.67E+1 9.00E-2 7.18E+2change solid-liquid 2.00E-2 2.00E-2 2.00E-2 export liquid to colloidal 2.25E+0 2.25E+0 2.25E+0change translational 6.20E+0 6.20E+0 6.20E+0 export mechanical 5.29E+0 2.10E-3 2.58E+1collect gas-gas 3.61E+0 3.61E+0 3.61E+0 export mixture 6.44E+0 5.28E-1 9.15E+0condition control 1.83E+0 1.83E+0 1.83E+0 export optical 6.31E+0 3.04E+0 1.12E+1condition electrical 1.83E+0 1.83E+0 1.83E+0 export pneumatic 1.54E+2 8.08E+0 7.18E+2convert chemical to mechanical 6.63E+0 6.63E+0 6.63E+0 export rotational 3.71E+0 1.95E-1 9.63E+0convert chemical to thermal 3.99E+2 6.63E+0 5.30E+2 export rotational to translational 2.25E+0 2.25E+0 2.25E+0convert control to status 1.57E+1 5.73E-1 3.60E+1 export signal 3.61E+0 3.61E+0 3.61E+0convert electrical 2.34E+0 9.00E-2 4.59E+0 export solid 1.21E+1 2.00E-2 7.18E+2convert electrical to electromagnetic 6.72E+0 1.62E-1 4.48E+1 export solid-liquid 7.18E+2 7.18E+2 7.18E+2convert electrical to mechanical 9.24E+0 5.00E-1 2.58E+1 export status 3.14E+1 5.73E-1 5.40E+1convert electrical to optical 1.81E+0 5.73E-1 3.04E+0 export thermal 4.49E+0 2.00E-2 1.97E+1convert electrical to rotational 9.39E+0 9.24E+0 1.20E+1 export translational 1.97E+1 1.97E+1 1.97E+1convert electrical to status 5.73E-1 5.73E-1 5.73E-1 guide electrical 2.38E+0 2.33E+0 2.50E+0convert electrical to thermal 4.04E-1 2.00E-2 8.08E+0 guide gas 1.34E+2 2.27E+0 7.18E+2convert electromagnetic to electrical 7.41E+0 3.61E+0 1.12E+1 guide human energy 1.10E+1 1.10E+1 1.10E+1convert electromagnetic to mechanical 2.21E-2 2.21E-2 2.21E-2 guide human material 3.45E+0 1.31E-2 1.10E+1convert gas to liquid 2.53E+1 8.08E+0 3.39E+1 guide hydraulic 6.07E+0 1.95E-1 1.34E+1convert human energy to control 2.01E+0 1.79E-1 1.34E+1 guide liquid 7.95E+0 9.00E-2 3.60E+1convert human energy to mechanical 5.26E+0 1.79E-1 2.58E+1 guide mechanical 5.84E+0 5.28E-1 1.97E+1convert human energy to rotational 3.81E+0 3.81E+0 3.81E+0 guide mixture 2.43E+2 5.28E-1 7.18E+2convert human material to control 8.20E-1 8.20E-1 8.20E-1 guide pneumatic 7.45E+0 6.20E+0 8.08E+0convert human material to mechanical 2.21E-2 2.21E-2 2.21E-2 guide radioactive/nuclear 1.12E+1 1.12E+1 1.12E+1convert liquid to colloidal 1.20E+1 1.20E+1 1.20E+1 guide rotational 5.73E+0 1.95E-1 1.97E+1convert liquid to gas 4.06E+0 2.00E-2 8.08E+0 guide signal 2.08E+1 2.08E+1 2.08E+1convert magnetic to control 3.61E+0 3.61E+0 3.61E+0 guide solid 6.17E+0 1.80E-3 7.18E+2convert magnetic to mechanical 2.21E-2 2.21E-2 2.21E-2 guide solid-gas 7.18E+2 7.18E+2 7.18E+2convert mechanical 9.26E+0 3.72E+0 1.55E+1 guide solid-liquid 5.47E+0 5.47E+0 5.47E+0convert mechanical to acoustic 8.31E+0 6.63E+0 9.15E+0 guide thermal 1.82E+2 8.08E+0 5.30E+2convert mechanical to electrical 2.02E+2 3.61E+0 5.30E+2 guide translational 9.95E+0 1.95E-1 1.97E+1convert mechanical to hydraulic 2.88E+1 1.20E+1 4.57E+1 import chemical 3.62E+2 6.63E+0 7.18E+2convert mechanical to pneumatic 1.14E+1 2.00E-1 3.60E+1 import control 1.84E+0 1.79E-1 1.12E+1convert mechanical to rotational 2.92E+0 2.92E+0 2.92E+0 import electrical 2.98E+0 2.10E-3 1.10E+1convert mechanical to status 5.28E-1 5.28E-1 5.28E-1 import gas 2.22E+2 2.00E-1 7.18E+2convert mechanical to thermal 2.68E+2 6.63E+0 5.30E+2 import human energy 2.70E+0 1.31E-2 2.58E+1convert pneumatic to mechanical 2.00E-1 2.00E-1 2.00E-1 import human material 2.63E+0 1.31E-2 1.97E+1convert pneumatic to rotational 2.00E-1 2.00E-1 2.00E-1 import hydraulic 2.93E+0 1.95E-1 8.08E+0convert pneumatic to translational 7.83E+0 2.00E-1 1.55E+1 import liquid 2.38E+1 2.00E-2 7.18E+2convert rotational to pneumatic 1.20E+1 1.20E+1 1.20E+1 import mechanical 3.96E+0 2.10E-3 1.97E+1convert rotational to translational 9.05E+0 1.95E-1 1.97E+1 import mixture 9.15E+0 9.15E+0 9.15E+0convert solid to liquid 1.20E+1 1.20E+1 1.20E+1 import optical 1.12E+1 1.12E+1 1.12E+1convert translational to rotational 1.11E+1 3.88E+0 1.97E+1 import pneumatic 1.88E+2 6.20E+0 7.18E+2couple electrical 4.59E+0 4.59E+0 4.59E+0 import rotational 4.01E+0 1.95E-1 1.97E+1couple solid 9.71E+0 1.80E-3 7.18E+2 import solid 7.93E+0 1.80E-3 7.18E+2

24

APPENDIX A (continued): Function-flow Failure Rates

Function-flow Wtd Avg Min Max Function-flow Wtd Avg Min Max

Fails/Mhours Fails/Mhours Fails/Mhours Fails/Mhours Fails/Mhours Fails/Mhours

import solid-liquid 2.94E+1 2.27E+0 1.92E+2 stop liquid to colloidal 2.25E+0 2.25E+0 2.25E+0import thermal 5.31E+0 6.12E-2 1.97E+1 stop material 5.40E+1 5.40E+1 5.40E+1import translational 9.63E+0 9.63E+0 9.63E+0 stop mixture 5.47E+0 5.47E+0 5.47E+0indicate control 5.73E-1 5.73E-1 5.73E-1 stop pneumatic 5.47E+0 5.47E+0 5.47E+0indicate electromagnetic 1.89E+1 5.73E-1 4.48E+1 stop rotational to translational 2.25E+0 2.25E+0 2.25E+0indicate signal 1.02E+0 1.62E-1 3.61E+0 stop solid 4.60E+0 1.95E-1 5.40E+1indicate status 1.34E+1 1.79E-1 5.40E+1 stop thermal 2.05E+0 6.12E-2 2.25E+0indicate visual 5.40E+1 5.40E+1 5.40E+1 store chemical 4.08E+0 4.08E+0 4.08E+0join solid 4.92E+0 1.95E-1 2.08E+1 store control 4.59E+0 4.59E+0 4.59E+0link solid 2.92E+0 2.92E+0 2.92E+0 store electrical 4.10E+0 4.08E+0 4.59E+0position human material 1.25E+1 1.10E+1 1.97E+1 store gas 1.92E+2 1.92E+2 1.92E+2position liquid 1.15E+1 9.63E+0 1.34E+1 store hydraulic 2.00E-1 2.00E-1 2.00E-1position mechanical 3.61E+0 3.61E+0 3.61E+0 store liquid 3.13E+0 2.25E+0 1.20E+1position solid 3.81E+0 1.80E-3 7.18E+2 store mechanical 1.52E+0 1.95E-1 1.97E+1process control 4.59E+0 4.59E+0 4.59E+0 store mixture 2.25E+0 2.25E+0 2.25E+0process electrical 3.61E+0 3.61E+0 3.61E+0 store pneumatic 6.20E+0 6.20E+0 6.20E+0process status 5.73E-1 5.73E-1 5.73E-1 store solid 3.87E+0 2.25E+0 1.20E+1regulate control 2.36E+0 8.20E-1 6.20E+0 store solid-liquid 2.25E+0 2.25E+0 2.25E+0regulate electrical 3.13E+0 9.00E-2 2.58E+1 supply electrical 3.94E+0 2.33E+0 4.59E+0regulate gas 9.55E+1 5.47E+0 5.30E+2 supply gas 1.92E+2 1.92E+2 1.92E+2regulate hydraulic 4.18E+0 4.23E-1 1.34E+1 supply hydraulic 2.00E-1 2.00E-1 2.00E-1regulate liquid 5.73E+0 4.23E-1 1.34E+1 supply liquid 3.33E+0 2.25E+0 1.20E+1regulate material 3.01E+1 6.20E+0 5.40E+1 supply mechanical 1.16E+0 1.95E-1 3.81E+0regulate mechanical 4.00E+0 1.80E-3 4.69E+0 support solid 1.46E+0 1.80E-3 2.92E+0regulate pneumatic 5.47E+0 5.47E+0 5.47E+0 transfer chemical 7.18E+2 7.18E+2 7.18E+2regulate solid 9.73E+1 4.57E+1 1.92E+2 transfer control 4.19E+0 1.80E-3 1.33E+1regulate thermal 1.33E+1 1.33E+1 1.33E+1 transfer electrical 3.42E+0 2.10E-3 9.24E+0secure human material 1.97E+1 1.97E+1 1.97E+1 transfer gas 1.56E+1 1.20E+1 3.39E+1secure mixture 9.15E+0 9.15E+0 9.15E+0 transfer human energy 9.87E+0 1.83E+0 1.10E+1secure solid 5.52E+0 1.80E-3 7.18E+2 transfer hydraulic 6.08E+0 2.00E-1 1.20E+1secure solid-liquid 1.92E+2 1.92E+2 1.92E+2 transfer liquid 2.66E+2 3.39E+1 7.18E+2sense control 4.10E+0 3.61E+0 4.59E+0 transfer mechanical 6.93E+0 1.80E-3 7.18E+2sense electrical 1.32E+1 1.32E+1 1.32E+1 transfer rotational 3.97E+0 9.30E-1 1.97E+1sense solid 4.98E+1 4.57E+1 5.40E+1 transfer signal 1.79E-1 1.79E-1 1.79E-1sense status 2.04E+1 3.61E+0 5.40E+1 transfer solid-liquid 2.49E+2 1.95E-1 7.18E+2sense thermal 8.45E+0 3.61E+0 1.33E+1 transfer status 3.61E+0 3.61E+0 3.61E+0separate gas 1.92E+2 1.92E+2 1.92E+2 transfer thermal 4.15E+0 1.90E-2 1.97E+1separate material 9.63E+1 5.00E-1 1.92E+2 transmit control 5.40E+1 5.40E+1 5.40E+1separate mixture 6.20E+0 6.20E+0 6.20E+0 transmit electrical 1.41E+1 1.90E-2 5.40E+1separate solid 6.65E+0 4.23E-1 9.15E+0 transmit human energy 1.02E+1 1.83E+0 1.97E+1shape solid 5.40E+1 5.40E+1 5.40E+1 transmit mechanical 7.86E+0 3.81E+0 2.08E+1stabilize mechanical 3.61E+0 3.61E+0 3.61E+0 transmit pneumatic 2.08E+1 2.08E+1 2.08E+1stop electrical 1.28E+0 6.12E-2 2.50E+0 transmit rotational 4.91E+0 1.95E-1 9.63E+0stop gas 4.45E+1 5.47E+0 1.92E+2 transmit thermal 6.63E+0 2.00E-2 1.97E+1stop hydraulic 5.47E+0 5.47E+0 5.47E+0 transport solid 1.47E+1 9.63E+0 1.97E+1stop liquid 5.39E+0 2.00E-2 1.34E+1

25

Link Between Function-Flow Failure Rates and Failure Modes for Early Design Stage Reliability Analysis

Authors

Bryan M. O’Halloran

100 Dearborn Hall


Robert B. Stone Ph.D

406 Rogers Hall


Irem Y. Tumer Ph.D

408 Rogers Hall


Proceedings of the 2011 ASME International Mechanical Engineering Congress and

Exposition

Safety Engineering, Risk Analysis, and Reliability Methods

IMECE 2011

November 11-17, 2011, Denver, CO, United States of America

26







ABSTRACT

The scope of this paper is to provide an extension to the Function Failure Design

Method (FFDM). We first implement a more robust knowledge base using Failure

Mode/Mechanism Distributions 1997 (FMD-97). Then failure rates from Nonelectric

Parts Reliability Data (NPRD-95) are added to more effectively determine the

likelihood that a failure mode will occur. The proposed Functional Failure Rate Design

Method (FFRDM) uses functional inputs to effectively offer recommendations to

mitigate failure modes that have a high likelihood of occurrence. This work uses a past

example where FFDM and Failure Modes and Effects Analysis (FMEA) were

compared to show that improvements have been made. A four step process is

presented to show how the FFRDM is used during conceptual design.

1. INTRODUCTION

In the process of design, functionality is where the voice of the customer is

captured. For this reason, failure can be defined as the loss of functionality [1].

Meaning that if the design stops working in the way the customer prefers, it has failed.

Since we design for functionality, data in this research has been tabulated to provide

designers the capability to perform accurate reliability analyses directly after

generating a functional model. Functional modeling is performed at the conceptual

stage of design before any components have been determined [2]. This data has been

carefully calculated using historical failure information and relationships between

functions and components. Although, here the failure rates are linked to specific

failure modes and offer the likelihood that the failure mode will occur given that a

specific function-flow appears in the functional model.

Performing reliability analysis at the conceptual level of design offers the power

of risk informed decision making to the designer. As the design process continues it

becomes increasingly expensive to make design changes. Providing an analysis that

can mitigate this problem at the conceptual level may significantly reduce the

likelihood of costly failure events.

27

2. BACKGROUND

This section provides a survey of the relevant related research. These topics

include Functional Modeling, FFDM, Risk in Early Design, and Failure Rates, Modes,

and Mechanisms.

2.1. Functional Modeling

Functional modeling is a standard part of many engineering design

methodologies and is used to describe a design at an abstract level. Generating a

functional model is done early in the design process before components have been

chosen in an original design problem or before reviewing existing component choices

in a redesign problem. The design process, in a general sense, follows five steps;

project definition and planning, specification definition, conceptual design, product

development, and product support [26]. The functional design method is used in the

first stage of conceptual design.

The format of functional models consists of functions connected by flows. The

three types of flow include material, energy, and signal. Stone [27] standardized

functional modeling by creating a common functional basis which provided a set

number of functions and flows to describe the entire design space. The functional basis

provides consistency across functional models of different designs. The functional

basis is used as the starting point for this research. Failure rates of failure modes are

found here for each term in the functional basis. Appendix A presents this data in a

summarized version due to page limit restrictions. This includes each functional basis

term.

Table 1 gives an example using nail clippers for how the Functional Basis is

different from describing a design using general functionality.

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TABLE 1: Example Using Functional Basis Terminology

General Functional Basis

- Accept user’s hand- Position user’s hand- Move clipper to desired location- Apply force on lever to actuate clipper- Return clippers to storage- Release user’s hand

- Import Human Energy- Import Human Material- Import Solid Material- Guide Solid Material- Position Solid Material- Actuate Solid Material- Guide Solid Material- Position Solid Material- Export Human Energy- Export Human Material- Export Solid Material

2.2. Function Failure Design Methodology

FFDM is a structured formulation of the function-failure analysis method

introduced by Tumer and Stone [3], and is used to perform failure analysis in the

conceptual design stage. This method also aids the designer by using a function-based

concept generator approach which helps streamline the design process [20]. The

proposed extension to FFDM, FFRDM, does not use this concept generation. Instead,

FFRDM is used only to inform the designer at the functional level of design. FFDM

utilizes knowledge bases which link product function to failure modes. The knowledge

base data is archived in the form of a function-component matrix and a component-

failure mode matrix. This reduces the need for a designer to have a large intellectual

knowledge base.

FFDM has several advantages including reduced high user workload, using an

archived failure knowledge base, being usable during functional design, using the

functional basis, component taxonomy, and failure mode taxonomy as a formalized

failure language, and is practical for electrical and mechanical systems [21].

Currently, FFDM lacks a strong component failure mode knowledge base. Only

63 failure mode occurrences have been observed in this framework previously [3].

Adding to the knowledge base provides confidence in the results. Using FMD-97 [28],

this research has added approximately 36,700 failure mode occurrences to the

component-failure mode matrix.

29

2.3. Risk in Early Design

Risk in Early Design (RED) is a conceptual design tool which uses functional

inputs to assess risk. An algorithm along with historical failure data is combine to

provide the designer failure modes, likelihood, and severity from the functional inputs.

The RED database is populated by three sources including functional models,

bill of materials, and failure reports. Bill of materials and failure reports provide the

component name and failure mode occurrence respectively. Data is converted using

naming taxonomies for failure modes [29], components [30], and functions [27] to

standardize the process. Each taxonomy is explicitly defined and defines the entire set

of potential names. Figure 1 shows how each source correlates to matrices EC, CF,

and EF. The matrix EF is produced by multiplying matrix EC by CF.

FIGURE 1: Red Database Population

This information can be used to determine the respective difference in

occurrence between failure modes for a specific function. Similarly it can be

determined which failure modes globally occurs with the greatest frequency.

Although, this can not be used to predict likelihood of a failure mode. The current CF

30

matrix has approximately 600 observed occurrences. The proposed method has

observed over 36,700 occurrences to provide more robust results. Using sixty times

the number of occurrences will give the designer confidence that the method is well

backed by a large knowledge base.

In addition to this calculation, RED provides calculations for failure severity

and likelihood. Failure severity was gathered through studying NASA, FMEA, and

risk engineering sources. These sources provide the foundation to generate the CF’

matrix using scores from 0 to 5, where 5 is the most severe. A similar matrix

calculation was performed as in Figure 1. The result is the occurrence of functional

failure severity. Failure likelihood was generated from a detailed list of component

failure occurrences. The failures were sorted low to high based on their occurrences.

These were also categorized in to a 0 to 5 scale and a matrix calculation was

performed to determine the likelihood of the functional failures.

The likelihood data was tabulated solely using failure occurrence. Likelihood

cannot be determined in the absence of time since failure is time dependent. While

strictly using occurrence data, common components will observe increased likelihood

because they are used more often. Less common components, which may have a

higher failure rate, could receive a lower likelihood value because their failures are

observed less often. The solution is to use failure rate information in the place of

recorded failure occurrence. The FFRDM knowledge base proposed in this research

provides failure rates of failure modes for specific functions. This is the necessary data

to generate quantitative likelihood results at the conceptual stage of design.

2.4. Failure Rates, Modes, and Mechanisms

Failure rate (λ) is a commonly used and well accepted variable found during risk

and reliability calculations. In general, (λ) is recorded in units of Failure/Million

Hours or Failure/Million Miles. This depends on the source and how the data was

collected.

A common problem in reliability engineering is how failures can be mitigated.

The root of this problem can be better understood by the cause and result of a failure.

31

Depending on the source, the terms failure mode and failure mechanism are defined

differently. Often, they are used interchangeably as the end state of a failure. Collins

uses the term failure mode as the physical process or processes that produce a failure

[31]. Blischke and Murthy define this as the description of a fault. Although, neither

provide a definition for failure mechanism. FMD-97 defines failure mode as the

observable consequence of failure. Here, this definition is adopted and is extended to

also include any change in behavior. FMD-97 defines failure mechanism as the

physical process which causes the failure. This definition will also be adopted.

A common vocabulary of failure modes has been developed for mechanical

systems by Collins [31]. Work done by Stone and Tumer [29] has provided a failure

mode taxonomy for both electrical and mechanical systems. The latter will be used

here to convert failure modes from those listed in FMD-97. Although, for mechanical

failure modes that appeared in both taxonomies, definitions/descriptions were

consulted from Collins text to gather more consensus.

2.5. Failure Modes and Effects Analysis

The goal of FMEA is to identify, evaluate, and prevent critical component or

functional failures [5]. FMEA can be performed in exactly the same manner using

either components or functions. Failure is commonly defined as a loss in functionality

and therefore this research focuses on FMEA using functions. Critical functions

receive a recommended schedule and action to reduce the failure mode risk. FMEA is

a tool used to analyze systems to gather information that a decision can be made from.

High risk functions are determined by the risk priority number (RPN). The

FMEA analysis starts by identifying a list of functions and their potential failure

modes. A list of functions can be produced from the functional model while a list of

components is produced from the detailed component design architecture. Failure

modes are determined by expert knowledge or extensive research of similar designs.

The RPN value is the product of three variables; occurrence, severity, and likelihood

of detection. Occurrence refers to the likelihood that the failure will occur, severity is

how bad the failure is, and likelihood of detection is how hard the failure is to detect.

32

From the list of potential failures, the occurrence, severity, and likelihood of detection

are scored on a scale of 1 to 10, resulting in an RPN value in the range of 0 to 1000.

The usefulness of FMEA as a design tool is to look at the RPN values relative to each

other and determine which functions need action taken and which do not. From this

analysis, the designer can determine the critical functions of a system and make design

changes accordingly.

Information for single failure mode input into the FMEA is not a long process.

This simply involves entering the function, an associated failure mode, then listing the

severity, detection, and occurrence values. These values are also subjective and can

lead to a poor analysis of critical failures. Although, to perform a complete FMEA for

the entire design can be very time consuming. This involves generating a list of

potential failure modes for each function. At a functional level this is not intuitive and

at a component level would require domain-specific expert knowledge. Some

functions, or components, can have over 50 distinct failure modes that should be

considered. Next, each failure mode must have the severity, detection, and occurrence

determined and recorded. Once this is done, it must be determined which functions

have too high of an RPN value, then recommended actions must be recorded. In all,

this analysis becomes very time consuming.

FMEA also requires expert engineers to properly perform. Experts have

acquired a knowledge base that only they have access to. Although, even the seasoned

professional can miss failure modes with high occurrences. Using a computerized

knowledge base solves this simple mistake. Experts have recorded data for years

which has been grouped in to a single data source. The data found in this research was

calculated using this historical failure rate data. Engineers with little experience in a

specific field can use this data to produce expert level results.

The research described in this paper provides a solution to FMEA. This can

reduce the time required by an expert, or in some cases, eliminate the need for an

expert altogether. In FFRDM the functional model is used to generate the relevant

failure modes for a design. Failure modes are provided with failure rates as a way to

accurately determine the occurrence. Calculating the RPN value is not needed. Prior

33

work has shown that final recommendations by FFDM can exceed those of FMEA [3].

This example is revisited to show that improvements have been made in the extension

from FFDM by providing further useful recommendation and discussing

recommendations given previously that had low occurrence values.

3. RESEARCH APPROACH

This section provides information and the steps followed to arrive at the

knowledge base for FFRDM. Two data sources were used as a starting point,

NPRD-95 and FMD-97. Failure modes in FMD-97 were converted to a failure mode

taxonomy. A repository of product information was used to generate function to

component relationships. These relationships in conjunction with NPRD-95 and

FMD-97 were used to build the knowledge base for FFRDM.

3.1. Component Failure Rate Data Source [32]

NPRD-95 was used as the source of the component failure rate data. NPRD-95

was put together by Reliability Information Analysis Center. This reference is an

ongoing effort to collect and provide high volumes of data from a variety of sources

including both military and commercial. This specifically includes warranty manuals,

government sponsored studies, published papers and reports, databases, and military

maintenance systems. From the previous publication, NPRD-91, 56% more data has

been acquired. A strong emphasis was put on data quality during the collection phase.

This was done by ensuring completeness of data, consistency of data, equipment

population tracking, failure verification, and characterization of operation histories.

Often data is discarded if it does not meet quality standards. This document did not

indicate failure modes or mechanisms. Failure, as observed in NPRD-95, is classified

generically under solving the symptoms of the failure. A part failed if, when it was

replaced, the failure symptoms were not present anymore.

Comprehensive indices are provided for background on the parts and sampling.

These include the component manufacturer, model or part number, nominal

performance specifications specific to each part, population tested, number of

34

operation hours, and number failed. The operating hours and number of parts failed is

used to generate failure rates for both specific components and component classes. For

example, a failure rate is provided for a specific type of actuator, then a combined

failure rate is given for the actuator class. The failure rate for each component class is

the sum of the total components failed for that class divided by the sum of the

operating hours for each component in that class. Calculating both types of data lets

the user employ the data at a generic or specific level.

This data was employed in the Component-failure mode matrix. A component

naming taxonomy was used to define the entire set of components that would be used

in both the function-component and component-failure mode matrix. This taxonomy

was also used to look up values in NPRD-95. For each component in the taxonomy

that also appeared in NPRD-95, a failure rate was recorded. For components that did

not match verbatim, definitions in the component naming taxonomy were used to

determine whether or not a failure rate value should be recorded.

3.2. Failure Modes and Mechanism Data Source [28]

FMD-97 is a document constructed by the Reliability Information Analysis

Center to provide high volumes of data on failure modes and mechanisms. This data is

collected from a variety of sources and presented in a single document. Failure modes

and mechanisms are given for electrical, electronic, mechanical, and

electromechanical parts and assemblies.

FMD-97 is the second edition of this document replacing FMD-91. Important

improvements have been made including a new algorithm used to combine data

sources and additional raw data that has been collected since the first edition was

published. These have significantly improved the quality of this document and the

usability of the data.

The data in FMD-97 was used to populate the component-failure mode matrix.

In the same manner as the component naming taxonomy, failure modes in this

document were fit to a failure mode taxonomy [29]. Definitions provided in the

35

taxonomy were used for justification when names were not verbatim. Also, the data

details section of FMD-97 offered additional information for this justification.

Four failure mode categories were created to accommodate those failure modes

which did not adequately fit to the taxonomy. These include control issue, unknown,

other, and artifact failure. A control issue is the loss in control or communication of the

design, but also includes signal losses. This does not indicate any sort of physical

failure necessarily. This could in many cases, for example, be a software failure. In a

sensor, this would be the inability to retrieve data stored on the sensor even though it

exists. Intermittent operation is also included here. The unknown category was listed

within FMD-97. Failures were recorded, but the cause and result was not. For obvious

reasons, this data could not be converted to anything listed in the failure mode

taxonomy and was therefore left as unknown. The other category was also a category

listed in FMD-97 and was reserved for failure modes which are rarely observed for a

component type. Although the occurrence of the other is high (see Appendix A for

data), the occurrence within this category for any given failure mode is very low. For

this reason the data within the other category in FMD-97 was added up and kept under

the listing other.

As described previously, failure modes and failure mechanisms are defined

differently in this research. FMD-97 provides both but does not distinguish between

the two within the data, even though the cause and result of a failure are significantly

different phenomenon in many cases. The category artifact failure was created to

parse out what were considered to be the cause of the failure. There does not currently

exist a failure mechanism taxonomy used for design. Parsing these out was done by

proving which were failure mechanisms. Any failure mode/mechanism listing in

FMD-97 with an artifact in it was added to the artifact failure category. When FMD-97

lists these failure modes/mechanisms under a component, the assumption is that the

listed artifact was the cause and not the result. For example, the component connector

has failed 8 times by a contact failing and 4 by wire fracturing. Both contact and wire

are artifacts of the component connector and were recorded as failure mechanisms.

Both Design and Workmanship were also grouped with artifact failure since their

36

names describes them as predating the failure. Listings with specific information such

as loss of capacitance or change in resistance are included as failure modes because

they imply a specific change in behavior. Those such as electrical failure and excessive

leakage are more general and were also defined as failure modes.

3.3. Repository Data

The Design Engineering Lab Repository (http://designengineeringlab.org/

delabsite/repository.html) at Oregon State University was used for function component

mapping and data structuring. A function-component matrix was queried from the

repository using terms from the functional basis and component naming taxonomy

[29].

The function-component matrix is used to capture the relationship between the

functions and component naming terms. The function-component matrix lists

component naming terms across the first row as column headers and function-flow

pairs down the first column. The matrix is then filled with the occurrences of the

number of times a function is solved by a component. The matrix is populated in a

column format where every occurrence is listed for a specific component before any

are listed for the next component. This is because functions are related to components

in the repository database and not the other way around. There are 164 components

from the component naming terms listed and 731 function-flows. The total number of

occurrences is 16,365.

37





FIGURE 2: Function-Component Matrix Snippet

The example function-component matrix snippet in Figure 2 shows convert

rotational to translational being solved twice by the coupler. Zeros in the matrix

indicate that there is no observed relationship in the repository of the particular

function-flow and component. The component naming terms along the first row of the

function-component matrix are specifically defined [24]. These terms line up with the

component classes listed in NPRD-95.

3.4. Converging Data Using Matrix Multiplication

Two matrices, discussed in section 3.1 through 3.3, were generated to create the

FFRDM knowledge base. Once the component-failure mode matrix was populated

with occurrences of the failure modes, each row was normalized. The failure rates,

recorded from NPRD-95 for each component, were listed adjacent to each component

name. Each cell containing the normalized failure mode occurrence was multiplied by

the component failure rate. This distributed the failure rate of a component between all

of its observed failure modes. The result of this calculation is the failure rate of a

failure mode for a specific component.

Function(Component-MatrixFailures/Mhours 192.0795 x 0.1949 2.2727 15.4501 0.1624 x xGenerated-On:-Wed-Jan-26-22:44:46-PST-2011 converter conveyer coupler cover crank digital-display diode distributorconvert-pneumatic-to-status 0 0 0 0 0 0 0 1convert-pneumatic-to-translational 0 0 0 0 1 0 0 0convert-radioactive/nuclear-to-chemical 0 0 0 0 0 0 0 0convert-radioactive/nuclear-to-control 0 0 0 0 0 0 0 0convert-radioactive/nuclear-to-electrical 0 0 0 0 0 0 0 0convert-rotational-to-acoustic 0 0 0 0 0 0 0 0convert-rotational-to-electrical 0 0 0 0 0 0 0 0convert-rotational-to-hydraulic 0 0 0 0 0 0 0 0convert-rotational-to-mechanical 0 0 0 0 0 0 0 0convert-rotational-to-pneumatic 0 0 0 0 0 0 0 0convert-rotational 0 0 0 0 0 0 0 0convert-rotational-to-status 0 0 0 1 0 0 0 0convert-rotational-to-translational 0 0 2 0 0 0 0 0convert-signal-to-status 0 0 0 0 0 0 0 0convert-signal-to-visual 0 0 0 0 0 1 0 0convert-solar-to-chemical 0 0 0 0 0 0 0 0convert-solar-to-electrical 2 0 0 0 0 0 0 0convert-solar-to-status 0 0 0 0 0 0 0 0convert-solar-to-thermal 1 0 0 0 0 0 0 0convert-solid-to-chemical 0 0 0 0 0 0 0 0convert-solid-to-liquid 0 0 0 0 0 0 0 0convert-solid 1 0 0 0 0 0 0 0convert-solid-to-solid(solid 0 0 0 0 0 0 0 0convert-status-to-analog 0 0 0 0 0 0 0 0convert-status-to-control 0 0 0 1 0 0 0 0convert-status-to-electrical 0 0 0 0 0 0 0 0

38

The next step was done by multiplying the function-component matrix by the

component-failure mode matrix. The function-component matrix is 731 cells by 165

cells and the component-failure mode matrix is 165 cells by 39 cells. As a result of the

large sized matrices, the matrix multiplication was carried out in Matlab. The results

were then exported back in to excel. The result of this calculation is the failure rate of

a failure mode for a specific function and therefore the knowledge base for FFRDM.

4. RESULTS

This section begins with a description of the FFRDM knowledge base.

FFRDM during the design process is then described using four steps. An example is

used to show how this process takes place. Recommendations are provided for this

example based on a functional model and the likelihood of occurrence.

4.1. Failure Mode Data

In Appendix A, the FFRDM knowledge base is presented in a table format.

Due to size restriction, data is presented for functions instead of function-flows. Figure

3 shows a snippet of the full data set. The top row are failure modes taken from the

failure modes taxonomy and the first column are function-flows from the functional

basis. The cells in the matrix are failure rates in failures per million hours. These

values represent the number of times a function-flow will fail in a specific failure

mode for every million hours of operation. Values of zero indicate that there does not

exist a relationship between a failure mode and function flow. It should be noted that

this work does not claim that functions have failure modes. Rather, this research has

found that functions are linked to components which have failure modes. The

function-component and component-failure mode relationships prove that a

relationship does exist between functions and failure modes. Although, it does not

make sense to say that the failure mode belongs to the function since it was observed

from a component failing.

39

FIGURE 3: Function-Failure Mode Matrix Snippet

In the component-failure mode matrix there were 41 components which had

both failure mode and failure rate information. There also exist function-flows in the

repository that have no observed occurrences. This results in some function-flows not

having data. This can be seen in Figure 3 for export translational to acoustic. FFRDM

can not provide data for these function-flows during the design process.

Since there are often many components that are a solution to a function-flow,

there are often several failure modes fit to each function-flow. In some cases there an

even distribution of failure modes for that particular function-flow. For example, in the

function-failure mode matrix convert electromagnetic to mechanical energy has 11

failure mode occurrences. Galling & Seizure has the lowest failure rate with a value

equal to 0.0001 failures per million hours while wear has the highest with a value

equal to 0.0015 failures per million hours. In this case there is no particular failure

mode that would stand out to the designer as needing to be mitigated. This case makes

it hard to provide any useful recommendations because none of the failure modes

stand out beyond any other. In other cases there is one or two distinct failure modes for

!"#$%&'#()*'+,!-&*./01'2/ $'..'3&'# $.-$4&#5 $.//6 )-%&5"/ )./%%&#5 &76-$% *-%$8("6 #'&3//96'.%0/*/$%.'7-5#/%&$ :;:::< : : : : : : :/96'.%05-3 :;:=:> :;::<? :;::=@ : :;:::= : :;::=A :/96'.%05-3(5-3 : : : : : : : :/96'.%08"7-#0/#/.5B :;::=? :;:::@ :;::=C :;:::= :;:::> : : :;:::=/96'.%08"7-#07-%/.&-* :;::<A :;:=>D :;:<@> :;:<=< :;:::= : : :/96'.%08B2.-"*&$ :;::@E :;::== :;:::> : : :;:::= :;:::E :/96'.%0*&F"&20%'0$'**'&2-* : : : : : : : :/96'.%0*&F"&2 :;:=C? :;::>@ :;::@> :;::=A :;::=A :;:::< :;:::? :;:::</96'.%0*&F"&2(5-3 :;::> :;:::< : : : : :;:::E :/96'.%0*&F"&2(*&F"&2 : : : : : : : :/96'.%07-5#/%&$ : : : : : : : :/96'.%07/$8-#&$-* :;:<<? :;:=@? :;:> :;:::A :;::=@ :;:::@ :;:::E :;:::C/96'.%07&9%"./ : :;:=CA :;:AEE : : :;:::= : :/96'.%0'6%&$-* :;:::< :;:==A : : : : : :/96'.%06#/"7-%&$ :;::D :;::=< :;:::A : : : :;::=A :/96'.%0.-2&'-$%&G/,#"$*/-. : :;:==< : : : : : :/96'.%0.'%-%&'#-* :;::C? :;:::? :;::=A :;:::> :;::== :;:::= : :;:::</96'.%0.'%-%&'#-*0%'0%.-#3*-%&'#-* : : : : : : : :/96'.%03&5#-* : : : : : : : :/96'.%03'*&2 :;:<A :;:A=@ :;:E<C :;::<A :;::<A :;:::@ : :;:::E/96'.%03'*&2(*&F"&2 : : : : : : : :/96'.%03%-%"3 :;::@? :;::== :;:<<< :;:::= :;:::> : : :;:::=/96'.%0%8/.7-* :;:=:@ :;::>? :;::@ : :;:::A :;:::= :;:::E :;:::>/96'.%0%.-#3*-%&'#-*0%'0-$'"3%&$ : : : : : : : :/96'.%0%.-#3*-%&'#-* :;:::= :;:::= :;:::? : : : : :

40

a specific function-flow which stand out significantly. The failure mode creep for

regulate solid has a value equal to 0.0219 failures per million hours. The next closest

value is 0.0037 failures per million hours. Here the designer can see that the failure

mode creep is the most likely to occur and would provide recommendations to

mitigate this failure mode. In most cases there is a distribution of failure mode data. In

this situation a few failure modes have either high or low likelihood values and several

have moderate likelihood values. Figure 4 shows data for secure solid where 19 failure

modes have been observed. Failure rate values range from 0.001 to 0.5901 failure per

million hours. For this function-flow there is a single failure mode that stands out,

wear, and several with moderate and low values. Recommendations would be

provided to mitigate wear, cracking, and creep.

FIGURE 4: Failure Mode Data for Secure Solid

0" 0.1" 0.2" 0.3" 0.4" 0.5" 0.6"

bonding"defect"

breakdown"

contamina9on"

control"issue"

corrosion"

cracking"

creep"

direct"chemical"a?ack"

ar9fact"failure"

fa9gue"

fre@ng"

galling"and"seizure"

impact"

latchBup"

noise"

other"

overstress"of"incorrect"cur"mag"

rupture"

spalling"

unknown"

voiding"

wear"

Failure(Rate((failures(per(million(hours)(

Secure(Solid(

41

4.2. Functional Failure Rate Design Method

This method is used during the conceptual stage of design when the functional

model is complete. The process to accomplish this is done in four steps. To validate

the steps to use the FFRDM knowledge base, a past FFDM example has been

revisited. In this example, FFDM was used during the design of a portable air

compressor to provide recommendation that would mitigate potential failures. In this

section it is used to outline the use of the four steps and the FFRDM knowledge base.

Step 1: Import function-flows from the functional model

Figure 5 shows the functional model for the portable air compressor.

FIGURE 5: Functional Model for Portable Air Compressor

This information is formatted into a table format as shown in Figure 6. It is

important to notice the import solid appears twice in the functional model and twice in

Figure 6. This must be true in order for step 3 of the methodology to generate accurate

results.

Import Solid Mat.

Import Rot. E.

Convert Rot. E. to

Pn. E

Import Human

Mat.

Import Gas Mat.

Import Solid Mat.

Couple Solid Mat.

Stabilize Solid Mat.

Export Solid Mat.

Separate Gas Mat.

Guide Gas Mat.

Export Gas Mat.

Export Th. E.

Distribute Th. E.

Guide Pn. E.

Export Pn. E.

Portable Air Compressor

42

FIGURE 6: FFDM Step #1 Snippet

Step 2: Look up function-flows in the FFRDM knowledge base

There will be several failure modes for each functional input and all should be

recorded for the most complete results. A snippet of the result of step #2 is shown in

Figure 7.


Step 3: Sum failure rate data for each failure mode

The failure rates in each column should be summed to yield a total failure rate

for each failure mode. This step sets the stage to determine which failure modes the

!"#$%&'#()*'+&,-'.%/012&,-'.%/.'%1%&'#1*&,-'.%/3",1#/,1%4.&1*&,-'.%/2'*&5&,-'.%/2'*&5$'"-*4/2'*&5$'#64.%/.'%1%&'#1*/%'/-#4",1%&$47-'.%/-#4",1%&$0"&54/-#4",1%&$5&2%.&8"%4/%34.,1*47-'.%/%34.,1*24-1.1%4/0120"&54/01247-'.%/0122%18&*&94/2'*&547-'.%/2'*&5

Function(flow/Failure0Mode contamination control0issue corrosion cracking creep artifact0failure fatigue frettingimport0gas 0.0001 0.0055 0.006 0.0018 0.0011 0.0036 0 0.0001import0rotational 0.0001 0 0.0106 0.0081 0.0217 0.0214 0.0006 0.0019import0human0material 0 0.0006 0.0033 0.023 0.0301 0.0732 0.022 0.0002import0solid 0.0104 0.0043 0.0331 0.0494 0.0946 0.0662 0.0034 0.0035import0solid 0.0104 0.0043 0.0331 0.0494 0.0946 0.0662 0.0034 0.0035couple0solid 0.0211 0.0943 0.5681 0.0652 4.2447 3.7973 0.0134 0.1068convert0rotational0to0pneumatic 0 0.0101 0.008 0.0004 0 0.0004 0 0export0pneumatic 0 0.0101 0.009 0.0012 0.0003 0.0018 0 0guide0pneumatic 0 0.0006 0.0011 0.0014 0.0009 0.0005 0 0distribute0thermal 0.0002 0.0005 0.0029 0.0035 0.0031 0.004 0 0.0002export0thermal 0.0002 0.0065 0.0105 0.0047 0.005 0.0066 0 0.0003separate0gas 0 0 0 0 0 0 0 0guide0gas 0.0002 0.0258 0.0221 0.0028 0.0014 0.0042 0 0.0001export0gas 0.0002 0.0106 0.0104 0.0027 0.0015 0.0038 0 0.0001stabilize0solid 0 0 0.0004 0.0001 0.0001 0.001 0 0export0solid 0.0066 0.0028 0.023 0.0315 0.0628 0.0464 0.0023 0.0023

43

designer should spend time to determine recommendations for. A snippet of this result

can be seen in Figure 8.


Step 4: Provide designer with recommendations based on summed failure rates

To provide useful recommendations from the failure modes with high

likelihood, definitions provided in the failure mode taxonomy must be consulted and

additional research should be performed. Definitions in the taxonomy offer details on

the physical phenomena that occurs during failure. Additional research can help the

designer to understand how the high likelihood failure modes occur in a general sense.

These were used to determine the additional recommendations in Table 3.

4.3. Design Recommendations

To validate the FFRDM knowledge base, a past FFDM example was used. It

should be noted that this was the design of a new product and was chosen to be

compatible with information in the original FFDM knowledge base. The FFRDM

knowledge base is not limited to failures from a specific domain and will offer

information not seen by the previous knowledge base. FMEA was also performed in

this example and compared with FFDM. It was determined that FFDM provides

similar recommendations as FMEA as well as others which were not predicted by

Function(flow/Failure0Mode contamination control0issue corrosion cracking creep artifact0failure fatigue frettingimport0gas 0.0001 0.0055 0.006 0.0018 0.0011 0.0036 0 0.0001import0rotational 0.0001 0 0.0106 0.0081 0.0217 0.0214 0.0006 0.0019import0human0material 0 0.0006 0.0033 0.023 0.0301 0.0732 0.022 0.0002import0solid 0.0104 0.0043 0.0331 0.0494 0.0946 0.0662 0.0034 0.0035import0solid 0.0104 0.0043 0.0331 0.0494 0.0946 0.0662 0.0034 0.0035couple0solid 0.0211 0.0943 0.5681 0.0652 4.2447 3.7973 0.0134 0.1068convert0rotational0to0pneumatic 0 0.0101 0.008 0.0004 0 0.0004 0 0export0pneumatic 0 0.0101 0.009 0.0012 0.0003 0.0018 0 0guide0pneumatic 0 0.0006 0.0011 0.0014 0.0009 0.0005 0 0distribute0thermal 0.0002 0.0005 0.0029 0.0035 0.0031 0.004 0 0.0002export0thermal 0.0002 0.0065 0.0105 0.0047 0.005 0.0066 0 0.0003separate0gas 0 0 0 0 0 0 0 0guide0gas 0.0002 0.0258 0.0221 0.0028 0.0014 0.0042 0 0.0001export0gas 0.0002 0.0106 0.0104 0.0027 0.0015 0.0038 0 0.0001stabilize0solid 0 0 0.0004 0.0001 0.0001 0.001 0 0export0solid 0.0066 0.0028 0.023 0.0315 0.0628 0.0464 0.0023 0.0023Sum 0.0495 0.176 0.7416 0.2452 4.5619 4.0966 0.0451 0.119

44

FMEA [3]. Here, the analysis has been done using the FFRDM knowledge base to

show that, in general, the same recommendations can be made as well as additional

recommendations. Also, in section 4.4 the likelihood of the failures is discussed as a

way to offer the designer information on which recommendations require more

attention than others.

This analysis shows that improvements in FFDM have been accomplished.

This is done first by verifying the same recommendations can be obtained that were

proposed by the original FFDM knowledge base. Table 2 shows the function-flows

along with the original recommendations for the portable air compressor.

TABLE 2: FFDM Example for a Portable Air Compressor

Function-flow Recommendation

Import GasImport Rot.E.Import HandImport solidCouple solidConvert Rot.E. to Pn.E.Export Pn.E.Guide Pn.E.Distribute Th.E.Export Th.E.Separate GasGuide GasExport GasStabilize SolidExport Solid

- Choose materials that can properly interact with air and water- Perform fatigue analysis on rotating components and housing- Include a filter screen on air inlet- Include bearings to support shaft- Choose a flexible material for the exhaust tube- Fin the endplate for better heat transfer- Choose a hardened material with clamping flats for input shaft- Perform extensive stress analysis on support feet

The recommendations provided in Table 2 were derived directly from the

failure modes returned by the function-flows. These same function-flows were queried

for the FFRDM knowledge base and returned all but one of the failure modes. The

missing failure mode was yielding which correlated to the perform extensive stress

analysis on support feet recommendation.

Along with these, other failure modes were discovered for which

recommendation should be provided. These include artifact failure, creep, and

unknown. Unknown is listed as a failure mode with a high likelihood but

45

recommendations will not be provided since none can be derived. Recommendations

that summarize these added failure modes can be found in Table 3.

TABLE 3: Additional Recommendations for the Portable Air Compressor

Failure Mode Recommendation

Artifact Failure

Creep

- Research air intake and shaft support selection to mitigate artifact failure- Simulate design/build prototype to verify design- Inspect and evaluate periodically during manufacturing to mitigate error- Perform Finite Element Analysis to locate stress concentrations

Artifact Failure, as described previously, is caused by either an artifact failing,

a poor design, or poor workmanship during the building process. This information

about artifact failure was used to reason about what recommendations should be

offered to the designer. The first three recommendations address this.

Creep can be described as the tendency of a solid material to undergo plastic

deformation over time due to high material stress. Finite Element Analysis (FEA) can

be used to identify these stresses bases on force inputs. It is recommended that once

the design has geometry, FEA be performed. This can be done for a rough sketch or

the final design. A variety of software packages can be used in conjunction with a solid

modeling program to reduce high user workload during this process. For example,

Patran is capable of importing Solidworks drawings, but can also be used to reproduce

physical geometries for FEA.

Although this recommendation does not mitigate a failure during functional

design, it offers information during functional design that will be used to mitigate

failure.

4.4. Failure Mode Likelihood

Recommendations have been provided based on the FFRDM knowledge base

by using the four step process. In this knowledge base a likelihood in the form of a

46

failure rate is provided for each failure mode. This is used to determine which failure

modes should receive the most attention during design based on the likelihood of

failure. The additional failure modes presented in section 4.3 were those with a high

likelihood. Wear is the only original failure mode that was considered to have a high

failure rate. The failure rates associated with the additional three failure modes along

with four of the five in the original example are summarized in Table 4. The top four

failure modes are significant because their failure rates are noticeably higher than the

others.

TABLE 4: Failure Rates of Failure Modes for Portable Air Compressor

Failure Mode Failure Rate (Failure per Million Hours)

UnknownCreepArtifact FailureWearCorrosionFrettingFatigue

5.24354.56194.09663.37140.74160.11900.0451

The predominate failures associated with air compressors include not building

a sufficient amount of discharge air at the specified pressure, not being able to achieve

the specified pressure, and bearing failures [33]. The first two are a direct result of

wear in the valves. The failure mode wear was initially given by FFDM and was also

given by FFRDM as one with a high likelihood. Also, bearing failure corresponds

directly to artifact failure. The first recommendation in Table 3 provides mitigation for

this failure event.

Of the original failure modes proposed by FFDM, corrosion, fretting, and

fatigue had a low likelihood of occurring. There are not related to predominate failure

which leads to the conclusion that the recommendations associated with these failure

modes are not likely to occur and can be discarded. Implementing likelihood to the

failure modes reduces unnecessary work during the design process and steers

designers to critical failure modes.

47

5. CONCLUSION

The Functional Failure Rate Design Method was generated and presented to

provide critical failure information in the conceptual design stage to reduce the

likelihood of failure. The data in this knowledge base shows the likelihood that a

function-flow fails in a specific failure mode and motivates reliability analysis at the

early stage of design. The FFRDM knowledge base is an extension of FFDM. Failure

rates of components have been added to make decisions for which failure modes

should be prioritized. A significant increase in data has also been used to expand the

knowledge base to provide robust results. To validate this addition, the FFRDM

knowledge base was used on a past FFDM example of a portable air compressor. This

analysis shows that improvements in FFDM have been accomplished by determining

additional failure modes which were originally overlooked. Recommendations were

provided for these failure modes.

6. FUTURE WORK

The data presented in FMD-97 lists failure mode occurrences for specific

components. In this research this data was converted from the listed failure modes in

FMD-97 to a failure mode taxonomy. These taxonomies, Collin’s on mechanical

failures and Stone and Tumer’s on both mechanical and electrical, list failure modes in

a single level. Formatting the taxonomy in this manner assumes that all failure modes

can be described at a single level. Although, if there is a lack of information at the time

the failure is observed, the definitions provided in the current taxonomy would likely

be too descriptive to adequately fit the failure. The failure mode taxonomy should be

restructured to assume a hierarchal format. This provided two distinct advantages.

First, when the failure is being inspected and recorded in to data records for use later,

it will not be necessary to fit a failure to a failure modes that is more detailed than the

inspection can offer. If only general information can be gathered about the failure, it

should only be recorded in such a manner. The Reliability Information Analysis Center

has also recognized this issue. Data that is not acquired to their standards must be

discarded. A hierarchal structure for failure modes will result in data being recorded

48

more accurately, providing more data useable during the design process. The second

advantage for a new format is that the designer can perform reliability analyses at

different levels of abstraction. Failure modes can be viewed at the highest level as a

material, energy, or signal failure. This structure will follow the functional basis. This

offers designers direction and information for later reliability analyses.

In addition, the FFRDM knowledge base should be entered in the repository in

the Design Lab at OSU. This would take the next step to automate this process,

reducing user workload to mitigate failure.

7. ACKNOWLEDGMENTS

This research was funded in part by DARPA (Subaward to FA8650-10-C-7079

with Palo Alto Research Center). The opinions, findings, conclusions, and

recommendations expressed are those of the authors and do not necessarily reflect the

views of the sponsors.

49

APPENDIX A: Fails/Mhours

bond

ing'de

fect

breakdow

n

contam

ination

control'issue

corrosion

cracking

creep

artifact'failure

fatig

ue

frettin

g

actuate 1.0E94 0 1.1E93 3.2E92 1.7E92 2.4E93 5.4E93 5.7E92 9.0E94 4.0E94allow 0 0 0 9.0E94 4.5E93 0 6.0E94 4.0E94 0 0change 1.4E92 0 3.2E93 7.6E93 1.1E91 4.9E92 1.2E91 8.1E92 1.9E92 4.7E92channel 0 0 0 0 0 0 1.0E94 1.0E94 0 0collect 0 0 0 2.0E94 0 7.2E93 2.4E93 5.0E94 0 0condition 0 0 0 0 4.0E94 8.0E94 3.0E93 5.6E93 0 1.2E93connect 0 0 0 0 1.2E93 3.0E94 1.0E94 7.0E94 0 0contain 0 0 0 0 2.0E94 0 0 4.0E94 0 0convert 9.0E94 1.0E94 9.5E93 2.8E91 3.6E91 5.4E92 1.4E91 1.6E91 1.2E92 4.1E93decrease 0 0 0 0 0 0 0 0 0 0decrement 0 0 0 0 0 0 0 0 0 0detect 0 0 0 2.0E94 0 0 0 5.0E94 0 0display 0 0 0 5.8E93 1.0E92 2.6E93 6.6E92 1.9E93 0 0distribute 7.0E94 0 1.0E93 1.3E92 3.1E92 2.3E92 2.0E92 1.7E92 1.0E93 3.0E93export 1.4E93 2.0E94 1.7E92 8.3E92 1.3E91 1.2E91 2.1E91 2.2E91 2.6E92 7.5E93extract 0 0 0 0 4.0E94 7.0E94 3.0E94 0 0 0guide 3.4E92 2.0E94 1.2E92 1.2E91 4.4E91 2.2E91 4.3E91 4.4E91 7.2E92 1.1E91import 1.5E93 9.0E94 2.2E92 3.3E92 1.0E91 1.7E91 2.8E91 3.2E91 4.5E92 9.1E93increase 0 0 0 0 0 0 0 0 0 0increment 0 0 1.0E93 1.0E94 0 0 0 7.0E94 0 0indicate 0 0 0 8.1E93 1.5E92 1.0E92 9.3E92 1.3E92 1.7E93 1.0E94inhibit 0 0 0 0 2.2E93 4.0E94 1.1E93 4.4E93 0 0join 3.0E94 0 1.0E94 1.1E93 1.1E92 9.2E93 2.6E92 3.3E92 4.0E94 1.6E93link 0 0 0 0 4.5E93 7.2E93 2.5E93 1.0E94 0 0measure 0 0 0 0 0 0 0 0 0 0mix 1.0E94 0 0 6.0E94 7.0E94 2.0E94 6.0E94 5.0E94 1.0E94 4.0E94position 5.8E93 2.2E93 2.1E92 4.5E92 2.2E91 2.2E91 3.2E91 4.1E91 4.5E92 2.8E92prevent 0 0 0 6.0E94 1.6E93 3.0E94 3.0E94 3.5E93 0 0process 0 0 1.0E93 3.0E94 0 5.6E93 0 1.2E93 0 0provision 0 0 0 0 0 0 0 0 0 0regulate 2.3E93 0 1.6E92 1.7E92 4.1E92 1.0E92 6.5E92 6.2E92 4.1E93 8.5E93remove 0 0 0 0 7.0E94 0 7.5E93 6.6E93 0 2.0E94rotate 0 0 0 1.0E92 8.0E93 4.0E94 0 4.0E94 0 0secure 7.7E93 1.0E93 2.4E92 1.1E91 2.6E91 3.8E91 3.6E91 2.4E91 2.4E92 2.1E92sense 0 0 7.6E93 4.9E93 7.2E93 3.0E93 4.6E92 1.7E92 1.7E93 0separate 0 0 3.5E93 6.0E94 7.0E94 7.7E93 1.9E92 6.5E93 8.0E94 1.0E94shape 0 0 0 3.8E93 6.8E93 1.8E93 4.4E92 1.2E93 0 0signal 0 0 0 0 2.0E94 0 0 4.0E94 0 0stabilize 0 0 0 2.0E94 4.0E94 1.0E94 1.0E94 1.5E93 0 0stop 3.0E94 0 3.0E94 9.1E93 6.6E92 8.6E92 1.0E91 7.8E92 1.6E93 1.0E93store 0 2.3E93 6.8E93 1.2E92 1.2E92 1.6E92 3.2E92 3.1E92 0 6.0E94supply 2.0E94 2.3E93 4.5E93 6.0E93 8.4E93 1.3E93 2.7E92 2.8E92 3.0E94 1.3E93support 0 0 1.0E94 0 4.7E93 7.0E94 1.5E93 3.2E93 8.0E94 1.0E94transfer 1.3E92 1.0E93 1.3E92 1.1E91 2.5E91 5.5E92 1.4E91 1.8E91 2.7E92 4.2E92translate 0 0 0 0 0 0 0 0 0 0transmit 5.0E94 0 1.0E94 7.4E93 2.1E92 7.4E93 7.4E92 1.6E92 7.0E94 2.5E93transport 0 0 0 5.0E93 4.0E93 2.0E94 0 2.0E94 0 0

50

APPENDIX A (continued): Fails/Mhours

&-11%#&'-#$

'2(%G3

,(

%04-*+

1-+*5:34

#"%2(

"+5(

,

HC(,2+,(22'"

)'%#*",,(*+'*3,,(#+'

0-&#%+3$(

,34+3,(

3#.#"/

#

C"%$%#&

/(-,

-*+3-+( >7>9:< 8 8 ?789:; =7<9:= 67=9:6 A789:; ;7?9:= 8 ?7B9:=-11"/ B789:; 8 8 ;789:; >789:; B789:; 6789:; 67@9:< 8 B789:;*5-#&( 67;9:= 8 8 B7A9:< 67?9:= 67?9:= 67>9:= 67<9:6 6789:; <7<9:6*5-##(1 8 8 8 8 8 8 8 6789:; 8 =789:;*"11(*+ 6789:; 8 8 8 8 67@9:< 8 @789:; 8 8*"#$%+%"# 8 8 8 8 8 B789:; 8 =7A9:< 8 67A9:<*"##(*+ 8 8 8 8 =789:; 8 6789:; ;789:; 8 =7?9:<*"#+-%# 8 8 8 8 8 8 8 6789:< 8 ?789:;*"#C(,+ @789:= ;789:; =789:= <769:= 6769:6 67@9:6 >7B9:< =7>9:6 8 ;7=9:6$(*,(-2( 8 8 8 8 8 8 8 8 8 8$(*,(0(#+ 8 8 8 8 8 8 8 8 8 8$(+(*+ 6789:; 8 8 8 8 67@9:< 8 @789:; 8 8$%241-D =789:; 8 8 8 =789:< 6789:; 8 A7>9:= 8 >769:<$%2+,%!3+( 67<9:= <789:; 67<9:< 6769:< B7?9:< 6769:= 67=9:< <789:= 8 @7@9:=(E4",+ >789:= 67>9:< ?7>9:< <769:< ?789:= B789:= ?7<9:< =7<9:6 8 >789:6(E+,-*+ 8 8 8 8 ;789:; 8 8 6769:< 8 ;7@9:<&3%$( @769:= 6769:< >789:< <769:= @769:= 67A9:6 <7@9:= ?769:6 8 67?9I8%04",+ >7@9:= 67>9:< 67=9:< =7?9:< ;7=9:= 67>9:6 A7=9:< =7>9:6 8 @7;9:6%#*,(-2( 8 8 8 8 8 8 8 8 8 8%#*,(0(#+ <789:; 8 8 8 <789:; 67>9:< 8 6789:; 8 ;789:;%#$%*-+( ;789:; 8 8 8 <789:< ?7?9:< =789:; @7B9:= 8 <769:=%#5%!%+ 6769:< 8 8 8 <789:; <789:; 6789:; A7;9:< 8 A7;9:<F"%# =7<9:= ;789:; 8 =789:; ;7>9:< A7A9:< 67<9:< <7>9:= 8 ?769:=1%#. 8 8 8 8 6789:; 8 8 ;789:; 8 ?789:;0(-23,( 8 8 8 8 8 8 8 8 8 80%E ?789:; 8 8 6789:; <789:; =789:; =789:; =7=9:< 8 ;769:<4"2%+%"# A7=9:= 67<9:< 67<9:< 67=9:= A7?9:= =7=9:6 67;9:= ;789:6 8 @789:64,(C(#+ ;789:; 8 8 8 =789:; 67<9:< 8 6789:= 8 A7;9:<4,"*(22 ;789:; 8 8 8 <789:; ;7;9:< 8 6789:< 8 A789:<4,"C%2%"# 8 8 8 8 8 8 8 8 8 8,(&31-+( <7<9:= 8 8 67?9:< 67@9:= ?7?9:= ;789:< @7;9:= 6789:; 6769:6,(0"C( 8 6789:; 8 8 A789:; =789:; ;789:; B7?9:< 8 <7A9:<,"+-+( 8 8 67=9:< 8 67=9:< 67A9:< 8 8 8 B789:;2(*3,( >7?9:= 6769:< ;7?9:< =769:= >7A9:= =769:6 67=9:= <7?9:6 8 A7A9:62(#2( 6789:< 8 8 8 67>9:< 67>9:= 8 ?769:= 8 67@9:=2(4-,-+( ;789:; 8 8 8 ?789:; @789:; =789:; 67=9:= 8 =7@9:=25-4( =789:; 8 8 8 67;9:< 8 8 ;7;9:= 8 ;7B9:<2%&#-1 8 8 8 8 8 B789:; 8 6789:< 8 ?789:;2+-!%1%G( 6789:; 8 8 8 8 =789:< 8 <789:< 8 67=9:<2+"4 =7@9:= ;789:; 8 8 67>9:= 67>9:= <769:< 67;9:6 8 67A9:62+",( 6789:= <789:; 67=9:< 8 67B9:= 67?9:6 B789:; <7?9:= 6789:; ?7?9:=23441D B7?9:< <789:; A789:; 6789:; 67>9:= 67;9:6 6789:< <789:= 8 <769:=2344",+ 6789:; 8 8 8 6789:; <789:; 8 67A9:< 8 >7B9:<+,-#2)(, ?7;9:= ?789:; >7?9:< =7=9:= ?7>9:= 67>9:6 67B9:= =789:6 8 A7>9:6+,-#21-+( 8 8 8 8 8 8 8 8 8 8+,-#20%+ 67>9:= =789:; 8 <789:; >7<9:< >7?9:< A789:; B7>9:= 8 6789:6+,-#24",+ 8 8 A789:; 8 A789:; B789:; 8 =769:< 8 =7B9:=

51

CONCLUSION The effort to move reliability engineering into the early stage of design

represents an increasing area of activity in engineering design. This research aims to

meet this need using two methodologies. The first methodology uses a RBD approach

during the functional stage of design. The second is a competitive alternative to

functional FMEA. Both move the risk analysis from its typical embodiment/redesign

stage to the front end of the design process.

Currently, failure rate data is available for components. Engineers typically use

component failure rates to evaluate design reliability or the mean-time-before-failure.

In this research a method is developed to calculate function-flow failure rates using

component failure rates. Using the Design Repository, a relationship was established

between the function-flows and components. Values in the matrix indicate the number

of occurrences where a component has solved a function-flow. Noise in the data was

eliminated using the Heaviside function. Two separate rules were implemented to

make this step systematic and logical. Component failure rates were shared with

function-flows based on a weighted average calculation, or a minimum and maximum

logic statement. This process can be reproduced using different components,

component failure rates, functional languages, occurrence data, or Heaviside rules.

Regardless, the outcome is a set of function-flow failure rates which can be

implemented using the methodology to calculate system reliability during function

design.

The methodology presented in the first manuscript provides useful information

to the designer during the function stage of design. This information can be used to

investigate different functions in the functional model, or to meet reliability design

requirements. The process to use the method consists of five steps and is performed

once the functional model is complete. Examples of the methodology were compared

with traditional RBDs. These show that minimum and maximum system reliability,

using the function-flow failure rates, are always less than or greater than that of the

traditional RBD. Also, in all three examples the weighted average reliability given by

the methodology showed similar results to those from the component failure rates.

52

Each was within 13% of the other. The goal of the weighted average reliability was to

mimic the reliability provided by the component RBD.

In the second manuscript, improvements were made to an existing process to

determine a relationship between functions and failure modes. The Design repository

was used to acquire the link between functions and components. A comprehensive

manual from the RIAC was used to generate a matrix linking components to failure

modes. Values in this matrix are the number of occurrences where a component has

failed in a certain failure mode. These occurrences were converted to failure rates by

multiplying through component failure rates. The final step is to multiply the two

matrices together. This returns a function to failure mode matrix. Any cell in this

matrix represents the failure rate of a failure mode for a specific function. This data

was calculated to be used in FFRDM, however the process to calculate the data can be

redone using different initial data.

Also in the second manuscript, FFRDM was presented to provide critical

failure information in the conceptual design stage to reduce the likelihood of failure.

The data in this knowledge base shows the likelihood that a function-flow fails in a

specific failure mode and motivates reliability analysis at the early stage of design.

The FFRDM knowledge base is an extension of FFDM. Failure rates of components

have been added to make decisions for which failure modes should be prioritized. A

significant increase in data has also been used to expand the knowledge base to

provide robust results. To validate this addition, the FFRDM knowledge base was used

on a past FFDM example of a portable air compressor. This analysis shows that

improvements in FFDM have been accomplished by determining additional failure

modes which were originally overlooked. Recommendations were provided for these

failure modes based on definition in the failure mode taxonomy and knowledge about

the product being designed.

Both methods presented in this thesis are used in the early stage of design.

Each method has specific capabilities, but each have the goal to provide designers

information earlier in the design process. This type of information helps the designer

53

become aware of potential failures and what parts of the design these failures result

from. Becoming aware of the potential failures is the first step to mitigating them.

54

VITABryan O'Halloran is currently a Master's of Science student in Mechanical

Engineering at Oregon State University and holds a Bachelor's of Science degree in

Engineering Physics from the same school. His current research interests are reliability

engineering and functional design.

55

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master's of science in mechanical engineering - thesis - ver 1

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