Factory Physics: The Science of Lean

Wallace HoppRoss School of BusinessUniversity of MichiganAnn Arbor, MI 48109

What is Lean?

• Waste elimination?

• A collection of practices (e.g., kanban)?

• A science?

• A philosophy?

Science of Flows

Definition: A flow is a sequence of processes and stockpoints(also called a “line” or a “routing”).

Science of Flows

1. Bottleneck Rate (rb): Rate of the work station with highest utilization, which defines capacity of system

rb

T0

2. Raw Process Time (T0): Sum of the average process times of each station in the line, which defines lower bound on cycle time

3. Critical WIP (W0 = rb × T0): Minimum amount of WIP required for line to operate at full capacity.

B

Better

Capability Curve – ThroughputTh

roug

hput

Work in Process

rb

W0

Best Case

Actual

Practical Worst Case Benchmark

Definition (Practical Worst Case): If the following conditions hold:1. Single-machine stations2. Balanced line3. Moderately high variability in process times

Then, the throughput for a given WIP level is given by

where W0 is the critical WIP.

,1

TH0

PWC brWIPWWIP

−+=

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16 18 20 22 24 26

TH

WIP

Capability Curves - Throughput

Best Caserb

1/T0

W0

Thro

ughp

ut

Work in Process

Chart4

000

111

222

333

444

555

666

777

888

999

101010

111111

121212

131313

141414

151515

161616

171717

181818

191919

202020

212121

222222

232323

242424

252525

262626

Best

Practical

Fab 2

WIP

TH

0.05

0.05

0.05

0.1

0.0888888889

0.097

0.15

0.12

0.14

0.2

0.1454545455

0.185

0.25

0.1666666667

0.225

0.3

0.1846153846

0.264

0.35

0.2

0.294

0.4

0.2133333333

0.315

0.4

0.225

0.332

0.4

0.2352941176

0.349

0.4

0.2444444444

0.361

0.4

0.2526315789

0.368

0.4

0.26

0.374

0.4

0.2666666667

0.379

0.4

0.2727272727

0.383

0.4

0.2782608696

0.386

0.4

0.2833333333

0.388

0.4

0.288

0.391

0.4

0.2923076923

0.393

0.4

0.2962962963

0.394

0.4

0.3

0.395

0.4

0.3034482759

0.3958

0.4

0.3066666667

0.3967

0.4

0.3096774194

0.397

Sheet1

Lead Time(days)T0 =20

Service in %2400260028003000rb =0.4

74W0 =8

757.591114.1

777.69.111.1514.3WIPBestPracticalWorstFab 2WIPBestPracticalWorstFab 2

797.719.2111.3114.53012020200.125

817.829.3211.4814.810.050.050.050.0522022.5400.4178932188

837.949.4411.715.0520.10.08888888890.050.09732025600.5476497308

858.099.611.9515.3530.150.120.050.1442027.5800.625

878.39.8212.2615.7540.20.14545454550.050.185520300.6777864045

898.471012.5716.150.250.16666666670.050.22562032.50.7167517095

918.710.2912.916.560.30.18461538460.050.264720350.747035527

938.9510.613.3517.0570.350.20.050.29482037.50.7714466094

959.3811.21417.780.40.21333333330.050.315922.5400.7916666667

9710.112.1314.918.790.40.2250.050.332102542.50.808772234

991113.216.320.5100.40.23529411760.050.3491127.5450.8234886554

100110.40.24444444440.050.361123047.50.8363248654

120.40.25263157890.050.3681332.5500.8476499019

130.40.260.050.374143552.50.8577387581

140.40.26666666670.050.3791537.5550.8668011103

150.40.27272727270.050.383164057.50.875

160.40.27826086960.050.3861742.5600.882464375

170.40.28333333330.050.388184562.50.8892977396

180.40.2880.050.3911947.5650.8955842661

190.40.29230769230.050.393205067.50.9013932023

200.40.29629629630.050.3942152.5700.9067821098

210.40.30.050.395225572.50.9117992836

220.40.30344827590.050.39582357.5750.9164855859

230.40.30666666670.050.3967246077.50.9208758548

240.40.30967741940.050.397

25

26

Sheet1

2400

2600

2800

3000

Service in %

Lead Time(days)

Sheet2

Best

Practical

Worst

Fab 2

WIP

TH

Sheet3

Benchmarking Example –HAL, Inc.

Large Panel Line: produces unpopulated printed circuit boards

Recent Performance:– Throughput = 1,400 panels per day (71.8 panels/hr)– WIP = 47,600 panels– Cycle Time = 34 days – Service = 75% on-time delivery

Is HAL lean?

HAL - Large Panel Line Processes

Lamination (Cores): press copper and prepreg into core blanksMachining: trim cores to sizeInternal Circuitize: etch circuitry into copper of coresOptical Test and Repair (Internal): scan panels optically for defectsLamination (Composites): press cores into multiple layer boardsExternal Circuitize: etch circuitry into copper on outside of compositesOptical Test and Repair (External): scan composites optically for defectsDrilling: holes to provide connections between layersCopper Plate: deposits copper in holes to establish connectionsProcoat: apply plastic coating to protect boardsSizing: cut panels into boardsEnd of Line Test: final electrical test

Layout of the Large Panel Line

HAL Capacity Data

Process Rate (p/hr) Time (hr) Lamination 191.5 4.7 Machining 186.2 0.5 Internal Circuitize 114.0 3.6 Optical Test/Repair - Int 150.5 1.0 Lamination – Composites 158.7 2.0 External Circuitize 159.9 4.3 Optical Test/Repair - Ext 150.5 1.0 Drilling 185.9 10.2 Copper Plate 136.4 1.0 Procoat 117.3 4.1 Sizing 126.5 1.1 EOL Test 169.5 0.5 rb, T0 114.0 33.9

Capacity: rb = 114 panels/dayRaw Process Time: T0 = 33.9 hoursCritical WIP: W0 = rbT0 = 114 × 33.9 = 3,869 panels

Process

Rate (p/hr)

Time (hr)

Lamination

191.5

4.7

Machining

186.2

0.5

Internal Circuitize

114.0

3.6

Optical Test/Repair - Int

150.5

1.0

Lamination – Composites

158.7

2.0

External Circuitize

159.9

4.3

Optical Test/Repair - Ext

150.5

1.0

Drilling

185.9

10.2

Copper Plate

136.4

1.0

Procoat

117.3

4.1

Sizing

126.5

1.1

EOL Test

169.5

0.5

rb, T0

114.0

33.9

HAL Case – PWC Comparison

System is not lean because of excess inventory

4.1051141869,3600,47

600,4710

=−+

=−+

= brWwwTH

Much higher than actual TH of 71.8!

TH Resulting from PWC with WIP = 47,600?

HAL Internal Benchmarking

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0 10,000 20,000 30,000 40,000 50,000

WIP

Thro

ughp

ut (p

anels

/hou

r)

BestWorstPWC

CurrentTH = 71.8WIP = 47,600“Lean" Region

“Fat" Region

PWC

Benchmarking Example –HAL Procoat• Procoat Process: coats panels with plastic coating

• Recent Performance:– WIP around 1500 panels – Throughput 1150 panels/day– Desired capacity of 3000 panels/day– Outside vendor being used to make up slack

Is Procoat lean?

HAL Procoat – Layout

Loader

BakeUnloader

UnloaderCoat 1Clean

D&IInspect

Touchup

Manufacturing Inspect

Loader

Expose

Clean Room

Coat 2

Develop

IN

OUT

HAL Procoat –Capacity Calculations

Capacity: rb = 2,879 panels/dayRaw Process Time: T0 = 546 min = 0.47 daysCritical WIP: W0 = rbT0 = 1,343 panels

Machine Name

Process or Load

Time (min)

Std Dev Process

Time (min)

Conveyor Trip Time

(min)

Number of

Machines MTTF MTTR AvailSetup Time

Rate (p/day)

Time (min)

Clean1 0.33 0 15 1 80 4 0.95 0 3377 36.5Coat1 0.33 0 15 1 80 4 0.95 0 3377 36.5Coat2 0.33 0 15 1 80 4 0.95 0 3377 36.5Expose 103 67 - 5 300 10 0.97 15 2879 121.9Develop 0.33 0 2.67 1 300 3 0.99 0 3510 22.7Inspect 0.5 0.5 - 2 - - 1.00 0 4680 0.5Bake 0.33 0 100 1 300 3 0.99 0 3510 121.0MI 161 64 - 8 - - 1.00 0 3488 161.0Touchup 9 0 - 1 - - 1.00 0 7800 9.0

2879 545.7

Sheet1

Batch Size60

Machine NameProcess or Load Time (min)Std Dev Process Time (min)Conveyor Trip Time (min)Number of MachinesMTTFMTTRAvailSetup TimeRate (p/day)Time (min)

Clean10.3301518040.950337736.5

Coat10.3301518040.950337736.5

Coat20.3301518040.950337736.5

Expose10367-5300100.97152879121.9

Develop0.3302.67130030.990351022.7

Inspect0.50.5-2--1.00046800.5

Bake0.330100130030.9903510121.0

MI16164-8--1.0003488161.0

Touchup90-1--1.00078009.0

2879545.7minutes

rbTo

Sheet2

Sheet3

HAL Procoat – Benchmarking

TH Resulting from PWC with WIP = 1,500:

520,1879,21343,1500,1

500,110

=−+

=−+

= brWwwTH

Much higher than actual TH of 1,150!

System is not lean because of insufficient capacity

HAL Procoat Case – Internal Benchmarking Outcome

-3000

300600900

12001500180021002400270030003300

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000WIP (panels)

Thro

ughp

ut (

pane

ls/d

ay)

Best Case

PWC

CurrentTH = 1,150 panels/dayWIP = 1,500 panels

“Lean” Region

“Fat” Region

Cause of Performance Degradation?Variability!

Suppliers Capacity CustomersInventory Inventory

Variability

Time

Variability

• Definition (Variability): Variability is anything that causes the system to depart from regular, predictable behavior.

• Sources of Variability:- machine failures - workpace variation- setups - differential skill levels- material shortages - material handling- yield loss - demand fluctuations- rework - engineering change orders- operator unavailability - product variety

May be consequence of business strategy

May be consequence of manufacturing practices

Variability and Queueing

rb

THQueue Time

Que

ue T

ime

Throughput

No variability

Variability

Better (less variability)

21

Principle (Queueing): At a single station with no limit on the number of entities that can queue up, the waiting time due to queueing is given by:

where V = variability factor, U = utilization, T = average process time for an entity at the station.

Queueing Theory

Queue Time = 𝑉𝑉 ×𝑈𝑈

1 − 𝑈𝑈× 𝑇𝑇

22

Variability Reduction

Variability Buffering

Principle (Variability Buffering): Variability in a production or supply chain system will be buffered by come combination of inventory, capacity and time.

Excess Inventory

Excess Capacity

Delay Time

Excess Inventory

Excess Capacity

Delay Time

Variability Buffering Examples

• Pens: variable demand– can’t buffer with time (backorder a pen?)– can’t buffer with capacity (too slow/expensive– must buffer with excess inventory

• Ambulance Service: variable demand/service– can’t buffer with inventory (service system)– can’t buffer with time (violates objectives)– must buffer with excess capacity

• Organ Transplants: variable supply/demand– can’t buffer with WIP (perishable)– can’t buffer with capacity (ethically anyway)– must buffer with delay time

Excess Inventory

Excess Capacity

Delay Time

The Factory Physics Prism

Definition of Lean

Definition (Lean): Production of goods and services is lean if it is accomplished with minimal buffering costs

Implication: lean involves variability reduction and buffer optimization

Toyota Improvement Cycle

Eliminatedirectwaste

Reduce variability

Reduce capacity buffers

Phase 1: Phase 2: Phase 3:

Substitute capacity for inventory

buffers

Phase 0:

“Two-shifting”Direct line supplyLean layoutBest practices

KanbanTQMTPM, etc.

3-shift operations

HAL Procoat Case

HAL Procoat – Layout

Loader

BakeUnloader

UnloaderCoat 1Clean

D&IInspect

Touchup

Manufacturing Inspect

Loader

Expose

Clean Room

Coat 2

Develop

IN

OUT

HAL Procoat – Capacity Data

Machine Name

Process or Load

Time (min)

Std Dev Process

Time (min)

Conveyor Trip Time

(min)

Number of

Machines MTTF MTTR AvailSetup Time

Rate (p/day)

Time (min)

Clean1 0.33 0 15 1 80 4 0.95 0 3377 36.5Coat1 0.33 0 15 1 80 4 0.95 0 3377 36.5Coat2 0.33 0 15 1 80 4 0.95 0 3377 36.5Expose 103 67 - 5 300 10 0.97 15 2879 121.9Develop 0.33 0 2.67 1 300 3 0.99 0 3510 22.7Inspect 0.5 0.5 - 2 - - 1.00 0 4680 0.5Bake 0.33 0 100 1 300 3 0.99 0 3510 121.0MI 161 64 - 8 - - 1.00 0 3488 161.0Touchup 9 0 - 1 - - 1.00 0 7800 9.0

2879 545.7

• Current throughput = 1150 panels/day

• Expose is bottleneck, but is underutilized (U = 1150/2879 = 40%)

• Coater is starving Expose (variability bottleneck?)

Sheet1

Batch Size60

Machine NameProcess or Load Time (min)Std Dev Process Time (min)Conveyor Trip Time (min)Number of MachinesMTTFMTTRAvailSetup TimeRate (p/day)Time (min)

Clean10.3301518040.950337736.5

Coat10.3301518040.950337736.5

Coat20.3301518040.950337736.5

Expose10367-5300100.97152879121.9

Develop0.3302.67130030.990351022.7

Inspect0.50.5-2--1.00046800.5

Bake0.330100130030.9903510121.0

MI16164-8--1.0003488161.0

Touchup90-1--1.00078009.0

2879545.7minutes

rbTo

Sheet2

Sheet3

The Factory Physics Prism

• Increase bottleneck capacity: break spelling at Expose

• Reduce bottleneck process variability: training at Expose

• Reduce arrival variability at bottleneck: field ready Coater parts

HAL Procoat – Outcome

0

500

1000

1500

2000

2500

3000

3500

0 1000 2000 3000 4000 5000

After

Before

Best Case

Practical Worst Case

Worst Case

WIP

TH

Applying Lean to Health Care

• Emergency Department Overcrowding– High utilization– High variability in arrivals and treatment– Long waits (4-5 hour average, much longer for low priority

patients)

• Improvement Options– Increase capacity (expensive)– Reduce variability

33

Arrival Variability Reduction

“Fast Pass” for Emergency Departments

Arrival Variability Reduction

Posting wait times so patients who can “smooth” will

Process Variability Reduction –Virtual Streaming of Patients

Conventional “pooling” protocol

New “virtual streaming” protocol

Metrics:

Time to first treatment (TTFT) for Admit (A) patients

Length of stay (LOS) for Discharge (D) patients

Note: ESI-2 patients are medically higher priority than ESI-3 patients

Benefits of Virtual Streaming

Results• TTFT for ESI-2 A patients (2A) gets 6 min worse, but gets 60 min better for 3A patients • LOS of ESI-2 D patients (2D) gets 2 min better and gets 88 min better for 3D patients

Reasons• Virtual Streaming reduces waiting variability by dividing capacity between streams• Physicians within streams can standardize policies (job shop/flow shop analogy)

Conclusions

• There is an underlying science to lean – the science of flows

• Capability curve analysis provides a form of internal benchmarking

• Variability and utilization combine to cause delay

• The factory physics prism provides a framework for applying lean to a wide range of systems

Diolch!

Factory Physics: �The Science of Lean��What is Lean?Science of FlowsScience of FlowsCapability Curve – ThroughputPractical Worst Case BenchmarkCapability Curves - ThroughputBenchmarking Example – �HAL, Inc.HAL - Large Panel Line ProcessesLayout of the Large Panel LineHAL Capacity DataHAL Case – PWC ComparisonHAL Internal BenchmarkingBenchmarking Example – �HAL ProcoatHAL Procoat – LayoutHAL Procoat – �Capacity CalculationsHAL Procoat – BenchmarkingHAL Procoat Case – Internal Benchmarking OutcomeCause of Performance Degradation?�Variability!VariabilityVariability and QueueingQueueing TheoryVariability BufferingVariability Buffering ExamplesThe Factory Physics PrismDefinition of Lean Toyota Improvement CycleHAL Procoat CaseHAL Procoat – LayoutHAL Procoat – Capacity DataThe Factory Physics PrismHAL Procoat – OutcomeApplying Lean to Health CareArrival Variability ReductionArrival Variability ReductionProcess Variability Reduction – �Virtual Streaming of PatientsBenefits of Virtual StreamingConclusionsSlide Number 39