Robust Optimization

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 ß 39 2.2.6.2 Computation of S/N and ß for L18 Data Sets 43 2.2.6.3 Response Table for S/N and ß 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 (ß) 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