Robust Optimization

Subir Chowdhury has been a thought leader in quality management strategy and methodology for more than 20 years. Currently Chairman and CEO of ASI Consulting Group, LLC, he leads Six Sigma and Quality Leadership implementation, and consulting and training efforts. Subir's work has earned him numerous awards and recognition. The New York Times cited him as a "leading quality expert"; BusinessWeek hailed him as the "Quality Prophet." The Conference Board Review described him as "an excitable, enthusiastic evangelist for quality."Subir has worked with many organizations across diverse industries including manufacturing, healthcare, food, and non-profit organizations. His client list includes major global corporations and industrial leaders such as American Axle, Berger Health Systems, Bosch, Caterpillar, Daewoo, Delphi Automotive Systems, Fiat-Chrysler Automotive, Ford, General Motors, Hyundai Motor Company, ITT Industries, Johns Manville, Kaplan Professional, Kia Motors, Leader Dogs for the Blind, Loral Space Systems, Make It Right Foundation, Mark IV Automotive, Procter & Gamble, State of Michigan, Thomson Multimedia, TRW, Volkswagen, Xerox, and more. Under Subir’s leadership, ASI Consulting Group has helped hundreds of clients around the world save billions of dollars in recovered productivity and increased revenues.Subir is the author of 14 books, including the international bestseller The Power of Six Sigma (Dearborn Trade, 2001), which has sold more than a million copies worldwide and been translated into more than 20 languages. Design for Six Sigma (Kaplan Professional, 2002) was the first book to popularize the "DFSS" concept. With quality pioneer Dr. Genichi Taguchi, Subir co-authored of two technical bestsellers Robust Engineering (McGraw Hill, 1999) and Taguchi's Quality Engineering Handbook (Wiley, 2005).His book, the critically acclaimed The Ice Cream Maker (Random House Doubleday, 2005) introduced LEO (Listen, Enrich, Optimize), a flexible management strategy that brings the concept of quality to every member of an organization. The book was formally recognized and distributed to every member of the 109th Congress. The LEO process continues to be implemented in many organizations. His most recent book, The Power of LEO (McGraw-Hill, 2011) was an Inc. Magazine bestseller. A follow-up to The Ice Cream Maker, the book shows organizations how the LEO methodology can be integrated into a complete quality management system. Shin Taguchi is Chief Technical Officer (CTO)for ASI Consulting Group, LLC.  He is a Master Black Belt in Six Sigma and Design for Six Sigma (DFSS) and was one of the world authorities in developing the DFSS program at ASI-CG, an internationally recognized training and consulting organization, dedicated to improving the competitive position of industries.  He is the son of Dr. Genichi Taguchi, developer of new engineering approaches for robust technology that have saved American industry billions of dollars.Over the last thirty years, Shin has trained more than 60,000 engineers around the world in quality engineering, product/process optimization, and robust design techniques, Mahalanobis-Taguchi System, known as Taguchi MethodsTM.  Some of the many clients he has helped to make products and processes Robust include:  Ford Motor Company, General Motors, Delphi Automotive Systems, Fiat-Chrysler Automotive, ITT, Kodak, Lexmark, Goodyear Tire & Rubber, General Electric, Miller Brewing, The Budd Company, Westinghouse, NASA, Texas Instruments, Xerox, Hyundai Motor Company, TRW and many others.  In 1996, Shin developed and started to teach a Taguchi Certification Course.  Over 360 people have graduated to date from this ongoing 16-day master certification course.Shin is a Fellow of the Royal Statistical Society in London, and is a member of the Institute of Industrial Engineering (IIE) and the American Society for Quality (ASQ); Shin is a member of the Quality Control Research Group of the Japanese Standards Association (JSA) and Quality Engineering Society of Japan. He is an editor of the Quality Engineering Forum Technical Journal and was awarded the Craig Award for the best technical paper presented at the annual conference of the ASQ.  Shin has been featured in the media through a number of national and international forums, including Fortune Magazine and Actionline (a publication of AIAG). Shin co-authored "Robust Engineering" published by McGraw Hill in 1999.  He has given presentations and workshops at numerous conferences, including ASQ, ASME, SME, SAE, and IIE.  He is also a Master Black Belt for Design for Six Sigma (DFSS).

• Preface xxiAcknowledgments xxvAbout the Authors xxvii1 Introduction to Robust Optimization 11.1 What Is Quality as Loss? 21.2 What Is Robustness? 41.3 What Is Robust Assessment? 51.4 What Is Robust Optimization? 51.4.1 Noise Factors 81.4.2 Parameter Design 91.4.3 Tolerance Design 132 Eight Steps for Robust Optimization and Robust Assessment 172.1 Before Eight Steps: Select Project Area 182.2 Eight Steps for Robust Optimization 192.2.1 Step 1: Define Scope for Robust Optimization 192.2.2 Step 2: Identify Ideal Function/Response 202.2.2.1 Ideal Function: Dynamic Response 202.2.2.2 Nondynamic Responses 212.2.3 Step 3: Develop Signal and Noise Strategies 232.2.3.1 How Input M is Varied to Benchmark “Robustness” 232.2.3.2 How Noise Factors Are Varied to Benchmark “Robustness” 232.2.4 Step 4: Select Control Factors and Levels 322.2.4.1 Traditional Approach to Explore Control Factors 322.2.4.2 Exploration of Design Space by Orthogonal Array 332.2.4.3 Try to Avoid Strong Interactions between Control Factors 332.2.4.4 Orthogonal Array and its Mechanics 362.2.5 Step 5: Execute and Collect Data 382.2.6 Step 6: Conduct Data Analysis 382.2.6.1 Computations of S/N and β 392.2.6.2 Computation of S/N and β for L18 Data Sets 432.2.6.3 Response Table for S/N and β 432.2.6.4 Determination of Optimum Design 482.2.7 Step 7: Predict and Confirm 492.2.7.1 Confirmation 502.2.8 Step 8: Lesson Learned and Action Plan 502.3 Eight Steps for Robust Assessment 522.3.1 Step 1: Define Scope 522.3.2 Step 2: Identify Ideal Function/Response and Step 3: Develop Signal and Noise Strategies 522.3.3 Step 4: Select Designs for Assessment 522.3.4 Step 5: Execute and Collect Data 522.3.5 Step 6: Conduct Data Analysis 522.3.6 Step 7: Make Judgments 532.3.7 Step 8: Lesson Learned and Action Plan 532.4 As You Go through Case Studies in This Book 553 Implementation of Robust Optimization 573.1 Introduction 573.2 Robust Optimization Implementation 573.2.1 Leadership Commitment 583.2.2 Executive Leader and the Corporate Team 583.2.3 Effective Communication 603.2.4 Education and Training 613.2.5 Integration Strategy 623.2.6 Bottom Line Performance 62PART ONE VEHICLE LEVEL OPTIMIZATION 634 Optimization of Vehicle Offset Crashworthy Design Using a Simplified AnalysisModel 65Chrysler LLC, USA4.1 Executive Summary 654.2 Introduction 664.3 Stepwise Implementation of DFSS Optimization for Vehicle Offset Impact 674.3.1 Step 1: Scope Defined for Optimization 674.3.2 Step 2: Identify/Select Design Alternatives 674.3.3 Step 3: Identify Ideal Function 684.3.4 Step 4: Develop Signal and Noise Strategy 694.3.4.1 Input and Output Signal Strategy 694.3.5 Step 5: Select Control/Noise Factors and Levels 704.3.5.1 Simplified Spring Mass Model Creation and Validation 704.3.5.2 Control Variable Selection 724.3.5.3 Control Factor Level Application for Spring Stiffness Updates 734.3.6 Step 6: Execute and Conduct Data Analysis 734.3.7 Step 7: Validation of Optimized Model 744.4 Conclusion 774.4.1 Acknowledgments 774.5 References 775 Optimization of the Component Characteristics for Improving Collision Safety by Simulation 79Isuzu Advanced Engineering Center, Ltd, Japan5.1 Executive Summary 795.2 Introduction 805.3 Simulation Models 815.4 Concept of Standardized S/N Ratios with Respect to Survival Space 825.5 Results and Consideration 865.6 Conclusion 945.6.1 Acknowledgment 945.7 Reference 94PART TWO SUBSYSTEMS LEVEL OPTIMIZATION BY ORIGINAL EQUIPMENT MANUFACTURERS (OEMs) 956 Optimization of Small DC Motors Using Functionality for Evaluation 97Nissan Motor Co., Ltd, Japan and Jidosha Denki Kogyo Co., Ltd, Japan6.1 Executive Summary 976.2 Introduction 986.3 Functionality for Evaluation in Case of DC Motors 986.4 Experiment Method and Measurement Data 996.5 Factors and Levels 1006.6 Data Analysis 1016.7 Analysis Results 1046.8 Selection of Optimal Design and Confirmation 1046.9 Benefits Gained 1076.10 Consideration of Analysis for Audible Noise 1086.11 Conclusion 1106.11.1 The Importance of Functionality for Evaluation 1106.11.2 Evaluation under the Unloaded (Idling) Condition 1106.11.3 Evaluation of Audible Noise (Quality Characteristic) 1116.11.4 Acknowledgment 1117 Optimal Design for a Double-Lift Window Regulator System Used in Automobiles 113Nissan Motor Co., Ltd, Japan and Ohi Seisakusho Co., Ltd, Japan7.1 Executive Summary 1137.2 Introduction 1147.3 Schematic Figure of Double-Lift Window Regulator System 1147.4 Ideal Function 1147.5 Noise Factors 1167.6 Control Factors 1177.7 Conventional Data Analysis and Results 1197.8 Selection of Optimal Condition and Confirmation Test Results 1207.9 Evaluation of Quality Characteristics 1227.10 Concept of Analysis Based on Standardized S/N Ratio 1247.11 Analysis Results Based on Standardized S/N Ratio 1257.12 Comparison between Analysis Based on Standardized S/N Ratio and Analysis Based on Conventional S/N Ratio 1277.13 Conclusion 1327.13.1 Acknowledgments 1327.14 Further Reading 1328 Optimization of Next-Generation Steering System Using Computer Simulation 133Nissan Motor Co., Ltd, Japan8.1 Executive Summary 1338.2 Introduction 1348.3 System Description 1348.4 Measurement Data 1358.5 Ideal Function 1368.6 Factors and Levels 1368.6.1 Signal and Response 1368.6.2 Noise Factors 1368.6.3 Indicative Factor 1378.6.4 Control Factors 1378.7 Pre-analysis for Compounding the Noise Factors 1378.8 Calculation of Standardized S/N Ratio 1388.9 Analysis Results 1418.10 Determination of Optimal Design and Confirmation 1418.11 Tuning to the Targeted Value 1428.12 Conclusion 1448.12.1 Acknowledgment 1459 Future Truck Steering Effort Robustness 147General Motors Corporation, USA9.1 Executive Summary 1479.2 Background 1489.2.1 Methodology 1489.2.2 Hydraulic Power-Steering Assist System 1499.2.3 Valve Assembly Design 1529.2.4 Project Scope 1539.3 Parameter Design 1549.3.1 Ideal Steering Effort Function 1549.3.2 Control Factors 1579.3.3 Noise Compounding Strategy and Input Signals 1579.3.4 Standardized S/N Post-Processing 1599.3.5 Quality Loss Function 1659.4 Acknowledgments 1729.5 References 17210 Optimal Design of Engine Mounting System Based on Quality Engineering 173Mazda Motor Corporation, Japan10.1 Executive Summary 17310.2 Background 17410.3 Design Object 17410.4 Application of Standard S/N Ratio Taguchi Method 17510.5 Iterative Application of Standard S/N Ratio Taguchi Method 17810.6 Influence of Interval of Factor Level 18110.7 Calculation Program 18410.8 Conclusions 18510.8.1 Acknowledgments 18610.9 References 18611 Optimization of a Front-Wheel-Drive Transmission for Improved Efficiency and Robustness 187Chrysler Group, LLC, USA and ASI Consulting Group, LLC, USA11.1 Executive Summary 18711.2 Introduction 18811.3 Experimental 18911.3.1 Ideal Function and Measurement 18911.4 Signal Strategy 19011.5 Noise Strategy 19111.6 Control Factor Selection 19211.7 Orthogonal Array Selection 19311.8 Results and Discussion 19611.8.1 S/N Calculations 19611.8.2 Graphs of Runs 20011.8.3 Response Plots 20111.8.4 Confirmation Run 20111.8.5 Verification of Results 20311.9 Conclusion 20611.9.1 Acknowledgments 20711.10 References 20712 Fuel Delivery System Robustness 209Ford Motor Company, USA12.1 Executive Summary 20912.2 Introduction 21012.2.1 Fuel System Overview 21012.2.2 Conventional Fuel System 21112.2.3 New Fuel System 21112.3 Experiment Description 21112.3.1 Test Method 21112.3.2 Ideal Function 21112.4 Noise Factors 21312.4.1 Control Factors 21312.4.2 Fixed Factors 21412.5 Experiment Test Results 21412.6 Sensitivity (β) Analysis 21412.7 Confirmation Test Results 21712.7.1 Bench Test Confirmation 21712.7.1.1 Initial Fuel Delivery System 21712.7.1.2 Optimal Fuel Delivery System 21812.7.2 Vehicle Verification 21812.7.2.1 Initial Fuel Delivery System 21912.7.2.2 Optimal Fuel Delivery System 21912.8 Conclusion 22013 Improving Coupling Factor in Vehicle Theft Deterrent Systems Using Design for Six Sigma (DFSS) 223General Motors Corporation, USA13.1 Executive Summary 22313.2 Introduction 22413.3 Objectives 22513.4 The Voice of the Customer 22513.5 Experimental Strategy 22513.5.1 Response 22513.5.2 Noise Strategy 22613.5.3 Control Factors 22613.5.4 Input Signal 22713.6 The System 22713.7 The Experimental Results 22813.8 Conclusions 22913.8.1 Summary 23313.8.2 Acknowledgments 234PART THREE SUBSYSTEMS LEVEL OPTIMIZATION BY SUPPLIERS 23514 Magnetic Sensing System Optimization 237ALPS Electric, Japan14.1 Executive Summary 23714.1.1 The Magnetic Sensing System 23814.2 Improvement of Design Technique 23914.2.1 Traditional Design Technique 23914.2.2 Design Technique by Quality Engineering 23914.3 System Design Technique 24114.3.1 Parameter Design Diagram 24114.3.2 Signal Factor, Control Factor, and Noise Factor 24214.3.3 Implementation of Parameter Design 24414.3.4 Results of the Confirmation Experiment 24414.4 Effect by Shortening of Development Period 24614.5 Conclusion 24614.5.1 Acknowledgments 24714.6 References 24715 Direct Injection Diesel Injector Optimization 249Delphi Automotive Systems, Europe and Delphi Automotive Systems, USA15.1 Executive Summary 24915.2 Introduction 25015.2.1 Background 25015.2.2 Problem Statement 25015.2.3 Objectives and Approach to Optimization 25115.3 Simulation Model Robustness 25315.3.1 Background 25315.3.2 Approach to Optimization 25715.3.3 Results 25715.4 Parameter Design 25715.4.1 Ideal Function 25715.4.2 Signal and Noise Strategies 25815.4.2.1 Signal Levels 25815.4.2.2 Noise Strategy 25815.4.3 Control Factors and Levels 25915.4.4 Experimental Layout 25915.4.5 Data Analysis and Two-Step Optimization 25915.4.6 Confirmation 26315.4.7 Discussions on Parameter Design Results 26415.4.7.1 Technical 26415.4.7.2 Economical 26415.5 Tolerance Design 26815.5.1 Signal Point by Signal Point Tolerance Design 26915.5.1.1 Factors and Experimental Layout 26915.5.1.2 Analysis of Variance (ANOVA) for Each Injection Point 26915.5.1.3 Loss Function 26915.5.2 Dynamic Tolerance Design 27015.5.2.1 Dynamic Analysis of Variance 27115.5.2.2 Dynamic Loss Function 27315.6 Conclusions 27515.6.1 Project Related 27515.6.2 Recommendations for Taguchi Methods 27715.6.3 Acknowledgments 27815.7 Reference and Further Reading 27816 General Purpose Actuator Robust Assessment and Benchmark Study 279Robert Bosch, LLC, USA16.1 Executive Summary 27916.2 Introduction 28016.3 Objectives 28016.3.1 Robust Assessment Measurement Method 28116.3.1.1 Test Equipment 28116.3.1.2 Data Acquisition 28416.3.1.3 Data Analysis Strategy 28516.4 Robust Assessment 28616.4.1 Scope and P-Diagram 28616.4.2 Ideal Function 28616.4.3 Signal and Noise Strategy 29016.4.4 Control Factors 29116.4.5 Raw Data 29116.4.6 Data Analysis 29116.5 Conclusion 29616.5.1 Acknowledgments 29716.6 Further Reading 29717 Optimization of a Discrete Floating MOS Gate Driver 299Delphi-Delco Electronic Systems, USA17.1 Executive Summary 29917.2 Background 30017.3 Introduction 30217.4 Developing the “Ideal” Function 30217.5 Noise Strategy 30517.6 Control Factors and Levels 30517.7 Experiment Strategy and Measurement System 30617.8 Parameter Design Experiment Layout 30617.9 Results 30717.10 Response Charts 30717.11 Two-Step Optimization 31117.12 Confirmation 31217.13 Conclusions 31217.13.1 Acknowledgments 31418 Reformer Washcoat Adhesion on Metallic Substrates 315Delphi Automotive Systems, USA18.1 Executive Summary 31518.2 Introduction 31618.3 Experimental Setup 31718.3.1 The Ideal Function 31818.3.2 P-Diagram 31818.3.3 Control Factors 31918.3.3.1 Alloy Composition 31918.3.3.2 Washcoat Composition 32018.3.3.3 Slurry Parameters 32018.3.3.4 Cleaning Procedures 32018.3.3.5 Preparation 32018.4 Control Factor Levels 32018.5 Noise Factors 32018.5.1 Signal Factor 32018.5.2 Unwanted Outputs 32018.6 Description of Experiment 32218.6.1 Furnace 32218.6.2 Orthogonal Array and Inner Array 32318.6.3 Signal-to-Noise and Beta Calculations 32318.6.4 Response Tables 32318.7 Two Step Optimization and Prediction 32318.7.1 Optimum Design 32918.7.2 Predictions 32918.8 Confirmation 32918.8.1 Design Improvement 32918.9 Measurement System Evaluation 33418.10 Conclusion 33418.11 Supplemental Background Information 33618.12 Acknowledgment 34018.13 Reference and Further Reading 34019 Making Better Decisions Faster: Sequential Application of Robust Engineering to Math-Models, CAE Simulations, and Accelerated Testing 341Robert Bosch Corporation, USA19.1 Executive Summary 34119.2 Introduction 34219.2.1 Thermal Equivalent Circuit – Detailed 34319.2.2 Thermal Equivalent Circuit – Simplified 34319.2.3 Closed Form Solution 34319.3 Objective 34519.3.1 Thermal Robustness Design Template 34519.3.2 Critical Design Parameters for Thermal Robustness 34519.3.3 Cascade Learning (aka Leveraged Knowledge) 34619.3.4 Test Taguchi Robust Engineering Methodology 34619.4 Robust Optimization 34719.4.1 Scope and P-Diagram 34719.4.2 Ideal Function 34719.4.3 Signal and Noise Strategy 34919.4.4 Input Signal 35019.4.5 Control Factors and Levels 35019.4.6 Math-Model Generated Data 35119.4.7 Data Analysis 35119.4.8 Thermal Robustness (Signal-to-Noise) 35419.4.9 Subsystem Thermal Resistance (Beta) 35619.4.10 Prediction and Confirmation 35719.4.11 Verification 36219.5 Conclusions 36419.5.1 Acknowledgments 36519.6 Futher Reading 36620 Pressure Switch Module Normally Open Feasibility Investigation and Supplier Competition 367Robert Bosch, LLC, USA20.1 Executive Summary 36720.2 Introduction 36820.2.1 Current Production Pressure Switch Module – Detailed 36820.2.2 Current Production (N.C.) Switching Element – Detailed 36920.3 Objective 37020.4 Robust Assessment 37020.4.1 Scope and P-Diagram 37020.4.2 Ideal Function 37120.4.3 Noise Strategy 37220.4.4 Testing Criteria 37220.4.5 Control Factors and Levels 37320.4.6 Test Data 37420.4.7 Data Analysis 37520.4.8 Prediction and Confirmation 37920.4.9 Verification 38320.5 Summary and Conclusions 38320.5.1 Acknowledgments 385PART FOUR MANUFACTURING PROCESS OPTIMIZATION 38721 Robust Optimization of a Lead-Free Reflow Soldering Process 389Delphi Delco Electronics Systems, USA and ASI Consulting Group, LLC, USA21.1 Executive Summary 38921.2 Introduction 39021.3 Experimental 39121.3.1 Robust Engineering Methodology 39121.3.2 Visual Scoring 39421.3.3 Pull Test 39621.4 Results and Discussion 39621.4.1 Visual Scoring Results 39621.4.2 Pull Test Results 40021.4.3 Next Steps 40121.5 Conclusion 40121.5.1 Acknowledgment 40221.6 References 40222 Catalyst Slurry Coating Process Optimization for Diesel Catalyzed Particulate Traps 403Delphi Energy and Chassis Systems, USA22.1 Executive Summary 40322.2 Introduction 40422.3 Project Description 40522.4 Process Map 40622.4.1 Initial Performance 40622.5 First Parameter Design Experiment 40622.5.1 Function Analysis 40722.5.2 Ideal Function 40922.5.3 Measurement System Evaluation 40922.5.4 Parameter Diagram 41122.5.5 Factors and Levels 41122.5.6 Compound Noise Strategy 41222.5.7 Parameter Design Experiment Layout (1) 41222.5.8 Means Plots 41422.5.9 Means Tables 41422.5.10 Two-Step Optimization and Prediction 41522.5.11 Predicted Performance Improvement Before and After 41622.6 Follow-up Parameter Design Experiment 41622.6.1 Parameter Design Experiment Layout (2) 41722.6.2 Means Plots for Signal-to-Noise Ratios 41722.6.3 Confirmation Results in Tulsa 41722.6.4 Noise Factor Q Affect on Slurry Coating 41722.7 Transfer to Florange 41922.7.1 Ideal Function and Parameter Diagram 42122.7.2 Parameter Design Experiment Layout (3) 42122.7.3 Means Plots for Signal-to-Noise Ratios 42322.7.4 Prediction and Confirmation 42322.7.5 Process Capability 42322.8 Conclusion 42422.8.1 The Team 424Index 427