Preface xxi
Acknowledgments xxv
About the Authors xxvii
1 Introduction to Robust Optimization 1
1.1 What Is Quality as Loss? 2
1.2 What Is Robustness? 4
1.3 What Is Robust Assessment? 5
1.4 What Is Robust Optimization? 5
1.4.1 Noise Factors 8
1.4.2 Parameter Design 9
1.4.3 Tolerance Design 13
2 Eight Steps for Robust Optimization and Robust Assessment 17
2.1 Before Eight Steps: Select Project Area 18
2.2 Eight Steps for Robust Optimization 19
2.2.1 Step 1: Define Scope for Robust Optimization 19
2.2.2 Step 2: Identify Ideal Function/Response 20
2.2.2.1 Ideal Function: Dynamic Response 20
2.2.2.2 Nondynamic Responses 21
2.2.3 Step 3: Develop Signal and Noise Strategies 23
2.2.3.1 How Input M is Varied to Benchmark “Robustness” 23
2.2.3.2 How Noise Factors Are Varied to Benchmark “Robustness” 23
2.2.4 Step 4: Select Control Factors and Levels 32
2.2.4.1 Traditional Approach to Explore Control Factors 32
2.2.4.2 Exploration of Design Space by Orthogonal Array 33
2.2.4.3 Try to Avoid Strong Interactions between Control Factors 33
2.2.4.4 Orthogonal Array and its Mechanics 36
2.2.5 Step 5: Execute and Collect Data 38
2.2.6 Step 6: Conduct Data Analysis 38
2.2.6.1 Computations of S/N and β 39
2.2.6.2 Computation of S/N and β for L18 Data Sets 43
2.2.6.3 Response Table for S/N and β 43
2.2.6.4 Determination of Optimum Design 48
2.2.7 Step 7: Predict and Confirm 49
2.2.7.1 Confirmation 50
2.2.8 Step 8: Lesson Learned and Action Plan 50
2.3 Eight Steps for Robust Assessment 52
2.3.1 Step 1: Define Scope 52
2.3.2 Step 2: Identify Ideal Function/Response and Step 3: Develop Signal and Noise Strategies 52
2.3.3 Step 4: Select Designs for Assessment 52
2.3.4 Step 5: Execute and Collect Data 52
2.3.5 Step 6: Conduct Data Analysis 52
2.3.6 Step 7: Make Judgments 53
2.3.7 Step 8: Lesson Learned and Action Plan 53
2.4 As You Go through Case Studies in This Book 55
3 Implementation of Robust Optimization 57
3.1 Introduction 57
3.2 Robust Optimization Implementation 57
3.2.1 Leadership Commitment 58
3.2.2 Executive Leader and the Corporate Team 58
3.2.3 Effective Communication 60
3.2.4 Education and Training 61
3.2.5 Integration Strategy 62
3.2.6 Bottom Line Performance 62
PART ONE VEHICLE LEVEL OPTIMIZATION 63
4 Optimization of Vehicle Offset Crashworthy Design Using a Simplified AnalysisModel 65
Chrysler LLC, USA
4.1 Executive Summary 65
4.2 Introduction 66
4.3 Stepwise Implementation of DFSS Optimization for Vehicle Offset Impact 67
4.3.1 Step 1: Scope Defined for Optimization 67
4.3.2 Step 2: Identify/Select Design Alternatives 67
4.3.3 Step 3: Identify Ideal Function 68
4.3.4 Step 4: Develop Signal and Noise Strategy 69
4.3.4.1 Input and Output Signal Strategy 69
4.3.5 Step 5: Select Control/Noise Factors and Levels 70
4.3.5.1 Simplified Spring Mass Model Creation and Validation 70
4.3.5.2 Control Variable Selection 72
4.3.5.3 Control Factor Level Application for Spring Stiffness Updates 73
4.3.6 Step 6: Execute and Conduct Data Analysis 73
4.3.7 Step 7: Validation of Optimized Model 74
4.4 Conclusion 77
4.4.1 Acknowledgments 77
4.5 References 77
5 Optimization of the Component Characteristics for Improving Collision Safety by Simulation 79
Isuzu Advanced Engineering Center, Ltd, Japan
5.1 Executive Summary 79
5.2 Introduction 80
5.3 Simulation Models 81
5.4 Concept of Standardized S/N Ratios with Respect to Survival Space 82
5.5 Results and Consideration 86
5.6 Conclusion 94
5.6.1 Acknowledgment 94
5.7 Reference 94
PART TWO SUBSYSTEMS LEVEL OPTIMIZATION BY ORIGINAL EQUIPMENT MANUFACTURERS (OEMs) 95
6 Optimization of Small DC Motors Using Functionality for Evaluation 97
Nissan Motor Co., Ltd, Japan and Jidosha Denki Kogyo Co., Ltd, Japan
6.1 Executive Summary 97
6.2 Introduction 98
6.3 Functionality for Evaluation in Case of DC Motors 98
6.4 Experiment Method and Measurement Data 99
6.5 Factors and Levels 100
6.6 Data Analysis 101
6.7 Analysis Results 104
6.8 Selection of Optimal Design and Confirmation 104
6.9 Benefits Gained 107
6.10 Consideration of Analysis for Audible Noise 108
6.11 Conclusion 110
6.11.1 The Importance of Functionality for Evaluation 110
6.11.2 Evaluation under the Unloaded (Idling) Condition 110
6.11.3 Evaluation of Audible Noise (Quality Characteristic) 111
6.11.4 Acknowledgment 111
7 Optimal Design for a Double-Lift Window Regulator System Used in Automobiles 113
Nissan Motor Co., Ltd, Japan and Ohi Seisakusho Co., Ltd, Japan
7.1 Executive Summary 113
7.2 Introduction 114
7.3 Schematic Figure of Double-Lift Window Regulator System 114
7.4 Ideal Function 114
7.5 Noise Factors 116
7.6 Control Factors 117
7.7 Conventional Data Analysis and Results 119
7.8 Selection of Optimal Condition and Confirmation Test Results 120
7.9 Evaluation of Quality Characteristics 122
7.10 Concept of Analysis Based on Standardized S/N Ratio 124
7.11 Analysis Results Based on Standardized S/N Ratio 125
7.12 Comparison between Analysis Based on Standardized S/N Ratio and Analysis Based on Conventional S/N Ratio 127
7.13 Conclusion 132
7.13.1 Acknowledgments 132
7.14 Further Reading 132
8 Optimization of Next-Generation Steering System Using Computer Simulation 133
Nissan Motor Co., Ltd, Japan
8.1 Executive Summary 133
8.2 Introduction 134
8.3 System Description 134
8.4 Measurement Data 135
8.5 Ideal Function 136
8.6 Factors and Levels 136
8.6.1 Signal and Response 136
8.6.2 Noise Factors 136
8.6.3 Indicative Factor 137
8.6.4 Control Factors 137
8.7 Pre-analysis for Compounding the Noise Factors 137
8.8 Calculation of Standardized S/N Ratio 138
8.9 Analysis Results 141
8.10 Determination of Optimal Design and Confirmation 141
8.11 Tuning to the Targeted Value 142
8.12 Conclusion 144
8.12.1 Acknowledgment 145
9 Future Truck Steering Effort Robustness 147
General Motors Corporation, USA
9.1 Executive Summary 147
9.2 Background 148
9.2.1 Methodology 148
9.2.2 Hydraulic Power-Steering Assist System 149
9.2.3 Valve Assembly Design 152
9.2.4 Project Scope 153
9.3 Parameter Design 154
9.3.1 Ideal Steering Effort Function 154
9.3.2 Control Factors 157
9.3.3 Noise Compounding Strategy and Input Signals 157
9.3.4 Standardized S/N Post-Processing 159
9.3.5 Quality Loss Function 165
9.4 Acknowledgments 172
9.5 References 172
10 Optimal Design of Engine Mounting System Based on Quality Engineering 173
Mazda Motor Corporation, Japan
10.1 Executive Summary 173
10.2 Background 174
10.3 Design Object 174
10.4 Application of Standard S/N Ratio Taguchi Method 175
10.5 Iterative Application of Standard S/N Ratio Taguchi Method 178
10.6 Influence of Interval of Factor Level 181
10.7 Calculation Program 184
10.8 Conclusions 185
10.8.1 Acknowledgments 186
10.9 References 186
11 Optimization of a Front-Wheel-Drive Transmission for Improved Efficiency and Robustness 187
Chrysler Group, LLC, USA and ASI Consulting Group, LLC, USA
11.1 Executive Summary 187
11.2 Introduction 188
11.3 Experimental 189
11.3.1 Ideal Function and Measurement 189
11.4 Signal Strategy 190
11.5 Noise Strategy 191
11.6 Control Factor Selection 192
11.7 Orthogonal Array Selection 193
11.8 Results and Discussion 196
11.8.1 S/N Calculations 196
11.8.2 Graphs of Runs 200
11.8.3 Response Plots 201
11.8.4 Confirmation Run 201
11.8.5 Verification of Results 203
11.9 Conclusion 206
11.9.1 Acknowledgments 207
11.10 References 207
12 Fuel Delivery System Robustness 209
Ford Motor Company, USA
12.1 Executive Summary 209
12.2 Introduction 210
12.2.1 Fuel System Overview 210
12.2.2 Conventional Fuel System 211
12.2.3 New Fuel System 211
12.3 Experiment Description 211
12.3.1 Test Method 211
12.3.2 Ideal Function 211
12.4 Noise Factors 213
12.4.1 Control Factors 213
12.4.2 Fixed Factors 214
12.5 Experiment Test Results 214
12.6 Sensitivity (β) Analysis 214
12.7 Confirmation Test Results 217
12.7.1 Bench Test Confirmation 217
12.7.1.1 Initial Fuel Delivery System 217
12.7.1.2 Optimal Fuel Delivery System 218
12.7.2 Vehicle Verification 218
12.7.2.1 Initial Fuel Delivery System 219
12.7.2.2 Optimal Fuel Delivery System 219
12.8 Conclusion 220
13 Improving Coupling Factor in Vehicle Theft Deterrent Systems Using Design for Six Sigma (DFSS) 223
General Motors Corporation, USA
13.1 Executive Summary 223
13.2 Introduction 224
13.3 Objectives 225
13.4 The Voice of the Customer 225
13.5 Experimental Strategy 225
13.5.1 Response 225
13.5.2 Noise Strategy 226
13.5.3 Control Factors 226
13.5.4 Input Signal 227
13.6 The System 227
13.7 The Experimental Results 228
13.8 Conclusions 229
13.8.1 Summary 233
13.8.2 Acknowledgments 234
PART THREE SUBSYSTEMS LEVEL OPTIMIZATION BY SUPPLIERS 235
14 Magnetic Sensing System Optimization 237
ALPS Electric, Japan
14.1 Executive Summary 237
14.1.1 The Magnetic Sensing System 238
14.2 Improvement of Design Technique 239
14.2.1 Traditional Design Technique 239
14.2.2 Design Technique by Quality Engineering 239
14.3 System Design Technique 241
14.3.1 Parameter Design Diagram 241
14.3.2 Signal Factor, Control Factor, and Noise Factor 242
14.3.3 Implementation of Parameter Design 244
14.3.4 Results of the Confirmation Experiment 244
14.4 Effect by Shortening of Development Period 246
14.5 Conclusion 246
14.5.1 Acknowledgments 247
14.6 References 247
15 Direct Injection Diesel Injector Optimization 249
Delphi Automotive Systems, Europe and Delphi Automotive Systems, USA
15.1 Executive Summary 249
15.2 Introduction 250
15.2.1 Background 250
15.2.2 Problem Statement 250
15.2.3 Objectives and Approach to Optimization 251
15.3 Simulation Model Robustness 253
15.3.1 Background 253
15.3.2 Approach to Optimization 257
15.3.3 Results 257
15.4 Parameter Design 257
15.4.1 Ideal Function 257
15.4.2 Signal and Noise Strategies 258
15.4.2.1 Signal Levels 258
15.4.2.2 Noise Strategy 258
15.4.3 Control Factors and Levels 259
15.4.4 Experimental Layout 259
15.4.5 Data Analysis and Two-Step Optimization 259
15.4.6 Confirmation 263
15.4.7 Discussions on Parameter Design Results 264
15.4.7.1 Technical 264
15.4.7.2 Economical 264
15.5 Tolerance Design 268
15.5.1 Signal Point by Signal Point Tolerance Design 269
15.5.1.1 Factors and Experimental Layout 269
15.5.1.2 Analysis of Variance (ANOVA) for Each Injection Point 269
15.5.1.3 Loss Function 269
15.5.2 Dynamic Tolerance Design 270
15.5.2.1 Dynamic Analysis of Variance 271
15.5.2.2 Dynamic Loss Function 273
15.6 Conclusions 275
15.6.1 Project Related 275
15.6.2 Recommendations for Taguchi Methods 277
15.6.3 Acknowledgments 278
15.7 Reference and Further Reading 278
16 General Purpose Actuator Robust Assessment and Benchmark Study 279
Robert Bosch, LLC, USA
16.1 Executive Summary 279
16.2 Introduction 280
16.3 Objectives 280
16.3.1 Robust Assessment Measurement Method 281
16.3.1.1 Test Equipment 281
16.3.1.2 Data Acquisition 284
16.3.1.3 Data Analysis Strategy 285
16.4 Robust Assessment 286
16.4.1 Scope and P-Diagram 286
16.4.2 Ideal Function 286
16.4.3 Signal and Noise Strategy 290
16.4.4 Control Factors 291
16.4.5 Raw Data 291
16.4.6 Data Analysis 291
16.5 Conclusion 296
16.5.1 Acknowledgments 297
16.6 Further Reading 297
17 Optimization of a Discrete Floating MOS Gate Driver 299
Delphi-Delco Electronic Systems, USA
17.1 Executive Summary 299
17.2 Background 300
17.3 Introduction 302
17.4 Developing the “Ideal” Function 302
17.5 Noise Strategy 305
17.6 Control Factors and Levels 305
17.7 Experiment Strategy and Measurement System 306
17.8 Parameter Design Experiment Layout 306
17.9 Results 307
17.10 Response Charts 307
17.11 Two-Step Optimization 311
17.12 Confirmation 312
17.13 Conclusions 312
17.13.1 Acknowledgments 314
18 Reformer Washcoat Adhesion on Metallic Substrates 315
Delphi Automotive Systems, USA
18.1 Executive Summary 315
18.2 Introduction 316
18.3 Experimental Setup 317
18.3.1 The Ideal Function 318
18.3.2 P-Diagram 318
18.3.3 Control Factors 319
18.3.3.1 Alloy Composition 319
18.3.3.2 Washcoat Composition 320
18.3.3.3 Slurry Parameters 320
18.3.3.4 Cleaning Procedures 320
18.3.3.5 Preparation 320
18.4 Control Factor Levels 320
18.5 Noise Factors 320
18.5.1 Signal Factor 320
18.5.2 Unwanted Outputs 320
18.6 Description of Experiment 322
18.6.1 Furnace 322
18.6.2 Orthogonal Array and Inner Array 323
18.6.3 Signal-to-Noise and Beta Calculations 323
18.6.4 Response Tables 323
18.7 Two Step Optimization and Prediction 323
18.7.1 Optimum Design 329
18.7.2 Predictions 329
18.8 Confirmation 329
18.8.1 Design Improvement 329
18.9 Measurement System Evaluation 334
18.10 Conclusion 334
18.11 Supplemental Background Information 336
18.12 Acknowledgment 340
18.13 Reference and Further Reading 340
19 Making Better Decisions Faster: Sequential Application of Robust Engineering to Math-Models, CAE Simulations, and Accelerated Testing 341
Robert Bosch Corporation, USA
19.1 Executive Summary 341
19.2 Introduction 342
19.2.1 Thermal Equivalent Circuit – Detailed 343
19.2.2 Thermal Equivalent Circuit – Simplified 343
19.2.3 Closed Form Solution 343
19.3 Objective 345
19.3.1 Thermal Robustness Design Template 345
19.3.2 Critical Design Parameters for Thermal Robustness 345
19.3.3 Cascade Learning (aka Leveraged Knowledge) 346
19.3.4 Test Taguchi Robust Engineering Methodology 346
19.4 Robust Optimization 347
19.4.1 Scope and P-Diagram 347
19.4.2 Ideal Function 347
19.4.3 Signal and Noise Strategy 349
19.4.4 Input Signal 350
19.4.5 Control Factors and Levels 350
19.4.6 Math-Model Generated Data 351
19.4.7 Data Analysis 351
19.4.8 Thermal Robustness (Signal-to-Noise) 354
19.4.9 Subsystem Thermal Resistance (Beta) 356
19.4.10 Prediction and Confirmation 357
19.4.11 Verification 362
19.5 Conclusions 364
19.5.1 Acknowledgments 365
19.6 Futher Reading 366
20 Pressure Switch Module Normally Open Feasibility Investigation and Supplier Competition 367
Robert Bosch, LLC, USA
20.1 Executive Summary 367
20.2 Introduction 368
20.2.1 Current Production Pressure Switch Module – Detailed 368
20.2.2 Current Production (N.C.) Switching Element – Detailed 369
20.3 Objective 370
20.4 Robust Assessment 370
20.4.1 Scope and P-Diagram 370
20.4.2 Ideal Function 371
20.4.3 Noise Strategy 372
20.4.4 Testing Criteria 372
20.4.5 Control Factors and Levels 373
20.4.6 Test Data 374
20.4.7 Data Analysis 375
20.4.8 Prediction and Confirmation 379
20.4.9 Verification 383
20.5 Summary and Conclusions 383
20.5.1 Acknowledgments 385
PART FOUR MANUFACTURING PROCESS OPTIMIZATION 387
21 Robust Optimization of a Lead-Free Reflow Soldering Process 389
Delphi Delco Electronics Systems, USA and ASI Consulting Group, LLC, USA
21.1 Executive Summary 389
21.2 Introduction 390
21.3 Experimental 391
21.3.1 Robust Engineering Methodology 391
21.3.2 Visual Scoring 394
21.3.3 Pull Test 396
21.4 Results and Discussion 396
21.4.1 Visual Scoring Results 396
21.4.2 Pull Test Results 400
21.4.3 Next Steps 401
21.5 Conclusion 401
21.5.1 Acknowledgment 402
21.6 References 402
22 Catalyst Slurry Coating Process Optimization for Diesel Catalyzed Particulate Traps 403
Delphi Energy and Chassis Systems, USA
22.1 Executive Summary 403
22.2 Introduction 404
22.3 Project Description 405
22.4 Process Map 406
22.4.1 Initial Performance 406
22.5 First Parameter Design Experiment 406
22.5.1 Function Analysis 407
22.5.2 Ideal Function 409
22.5.3 Measurement System Evaluation 409
22.5.4 Parameter Diagram 411
22.5.5 Factors and Levels 411
22.5.6 Compound Noise Strategy 412
22.5.7 Parameter Design Experiment Layout (1) 412
22.5.8 Means Plots 414
22.5.9 Means Tables 414
22.5.10 Two-Step Optimization and Prediction 415
22.5.11 Predicted Performance Improvement Before and After 416
22.6 Follow-up Parameter Design Experiment 416
22.6.1 Parameter Design Experiment Layout (2) 417
22.6.2 Means Plots for Signal-to-Noise Ratios 417
22.6.3 Confirmation Results in Tulsa 417
22.6.4 Noise Factor Q Affect on Slurry Coating 417
22.7 Transfer to Florange 419
22.7.1 Ideal Function and Parameter Diagram 421
22.7.2 Parameter Design Experiment Layout (3) 421
22.7.3 Means Plots for Signal-to-Noise Ratios 423
22.7.4 Prediction and Confirmation 423
22.7.5 Process Capability 423
22.8 Conclusion 424
22.8.1 The Team 424
Index 427
