Introduction to Engineering Statistics and Six SIGMA : Statistical Quality Control and Design of Experiments and Systems

List of Acronyms xxi 1 Introduction 1(28) 1.1 Purpose of this Book 1(1) 1.2 Systems and Key Input Variables 2(4) 1.3 Problem-solving Methods 6(4) 1.3.1 What Is "Six Sigma"? 7(3) 1.4 History of "Quality" and Six Sigma 10(8) 1.4.1 History of Management and Quality 10(4) 1.4.2 History of Documentation and Quality 14(1) 1.4.3 History of Statistics and Quality 14(3) 1.4.4 The Six Sigma Movement 17(1) 1.5 The Culture of Discipline 18(2) 1.6 Real Success Stories 20(1) 1.7 Overview of this Book 21(1) 1.8 References 22(1) 1.9 Problems 22(7) Part I Statistical Quality Control 2 Statistical Quality Control and Six Sigma 29(16) 2.1 Introduction 29(1) 2.2 Method Names as Buzzwords 30(1) 2.3 Where Methods Fit into Projects 31(2) 2.4 Organizational Roles and Methods 33(1) 2.5 Specifications: Nonconforming vs Defective 34(2) 2.6 Standard Operating Procedures (SOPs) 36(4) 2.6.1 Proposed SOP Process 37(3) 2.6.2 Measurement SOPs 40(1) 2.7 References 40(1) 2.8 Problems 41(4) 3 Define Phase and Strategy 45(30) 3.1 Introduction 45(1) 3.2 Systems and Subsystems 46(1) 3.3 Project Charters 47(4) 3.3.1 Predicting Expected Profits 50(1) 3.4 Strategies for Project Definition 51(2) 3.4.1 Bottleneck Subsystems 51(1) 3.4.2 Go-no-go Decisions 52(1) 3.5 Methods for Define Phases 53(5) 3.5.1 Pareto Charting 53(3) 3.5.2 Benchmarking 56(2) 3.6 Formal Meetings 58(2) 3.7 Significant Figures 60(3) 3.8 Chapter Summary 63(2) 3.9 References 65(1) 3.10 Problems 65(10) 4 Measure Phase and Statistical Charting 75(42) 4.1 Introduction 75(1) 4.2 Evaluating Measurement Systems 76(9) 4.2.1 Types of Gauge R&R Methods 77(1) 4.2.2 Gauge R&R: Comparison with Standards 78(3) 4.2.3 Gauge R&R (Crossed) with Xbar & R Analysis 81(4) 4.3 Measuring Quality Using SPC Charting 85(2) 4.3.1 Concepts: Common Causes and Assignable Causes 86(1) 4.4 Commonality: Rational Subgroups, Control Limits, and Startup 87(2) 4.5 Attribute Data: p-Charting 89(5) 4.6 Attribute Data: Demerit Charting and u-Charting 94(4) 4.7 Continuous Data: Xbar & R Charting 98(7) 4.7.1 Alternative Continuous Data Charting Methods 104(1) 4.8 Chapter Summary and Conclusions 105(2) 4.9 References 107(1) 4.10 Problems 107(10) 5 Analyze Phase 117(18) 5.1 Introduction 117(1) 5.2 Process Mapping and Value Stream Mapping 117(4) 5.2.1 The Toyota Production System 120(1) 5.3 Cause and Effect Matrices 121(2) 5.4 Design of Experiments and Regression (Preview) 123(2) 5.5 Failure Mode and Effects Analysis 125(3) 5.6 Chapter Summary 128(1) 5.7 References 129(1) 5.8 Problems 129(6) 6 Improve or Design Phase 135(12) 6.1 Introduction 135(1) 6.2 Informal Optimization 136(1) 6.3 Quality Function Deployment (QFD) 137(3) 6.4 Formal Optimization 140(3) 6.5 Chapter Summary 143(1) 6.6 References 143(1) 6.7 Problems 143(4) 7 Control or Verify Phase 147(14) 7.1 Introduction 147(1) 7.2 Control Planning 148(3) 7.3 Acceptance Sampling 151(4) 7.3.1 Single Sampling 152(1) 7.3.2 Double Sampling 153(2) 7.4 Documenting Results 155(1) 7.5 Chapter Summary 156(1) 7.6 References 157(1) 7.7 Problems 157(4) 8 Advanced SQC Methods 161(14) 8.1 Introduction 161(1) 8.2 EWMA Charting for Continuous Data 162(3) 8.3 Multivariate Charting Concepts 165(3) 8.4 Multivariate Charting (Hotelling's T² Charts) 168(4) 8.5 Summary 172(1) 8.6 References 172(1) 8.7 Problems 172(3) 9 SQC Case Studies 175(24) 9.1 Introduction 175(1) 9.2 Case Study: Printed Circuit Boards 175(6) 9.2.1 Experience of the First Team 177(2) 9.2.2 Second Team Actions and Results 179(2) 9.3 Printed Circuitboard: Analyze, Improve, and Control Phases 181(3) 9.4 Wire Harness Voids Study 184(5) 9.4.1 Define Phase 185(1) 9.4.2 Measure Phase 185(2) 9.4.3 Analyze Phase 187(1) 9.4.4 Improve Phase 188(1) 9.4.5 Control Phase 188(1) 9.5 Case Study Exercise 189(5) 9.5.1 Project to Improve a Paper Air Wings System 190(4) 9.6 Chapter Summary 194(1) 9.7 References 195(1) 9.8 Problems 195(4) 10 SQC Theory 199(42) 10.1 Introduction 199(1) 10.2 Probability Theory 200(3) 10.3 Continuous Random Variables 203(17) 10.3.1 The Normal Probability Density Function 207(5) 10.3.2 Defects Per Million Opportunities 212(1) 10.3.3 Independent, Identically Distributed and Charting 213(3) 10.3.4 The Central Limit Theorem 216(3) 10.3.5 Advanced Topic: Deriving d2 and c4 219(1) 10.4 Discrete Random Variables 220(5) 10.4.1 The Geometric and Hypergeometric Distributions 222(3) 10.5 Xbar Charts and Average Run Length 225(4) 10.5.1 The Chance of a Signal 225(2) 10.5.2 Average Run Length 227(2) 10.6 OC Curves and Average Sample Number 229(4) 10.6.1 Single Sampling OC Curves 230(1) 10.6.2 Double Sampling 231(1) 10.6.3 Double Sampling Average Sample Number 232(1) 10.7 Chapter Summary 233(1) 10.8 References 234(1) 10.9 Problems 234(7) Part II Design of Experiments (DOE) and Regression 11 DOE: The Jewel of Quality Engineering 241(18) 11.1 Introduction 241(1) 11.2 Design of Experiments Methods Overview 242(1) 11.2.1 Method Choices 242(1) 11.3 The Two-sample T-test Methodology and the Word "Proven" 243(3) 11.4 T-test Examples 246(3) 11.4.1 Second T-test Application 247(2) 11.5 Randomization and Evidence 249(1) 11.5.1 Poor Randomization and Waste 249(1) 11.6 Errors from DOE Procedures 250(2) 11.6.1 Testing a New Drug 252(1) 11.7 Chapter Summary 252(2) 11.7.1 Student Retention Study 253(1) 11.8 Problems 254(5) 12 DOE: Screening Using Fractional Factorials 259(26) 12.1 Introduction 259(1) 12.2 Standard Screening Using Fractional Factorials 260(6) 12.3 Screening Examples 266(5) 12.3.1 More Detailed Application 269(2) 12.4 Method Origins and Alternatives 271(4) 12.4.1 Origins of the Arrays 271(2) 12.4.2 Experimental Design Generation 273(1) 12.4.3 Alternatives to the Methods in this Chapter 273(2) 12.5 Standard vs One-factor-at-a-time Experimentation 275(2) 12.5.1 Printed Circuit Board Related Method Choices 277(1) 12.6 Chapter Summary 277(1) 12.7 References 277(1) 12.8 Problems 278(7) 13 DOE: Response Surface Methods 285(36) 13.1 Introduction 285(1) 13.2 Design Matrices for Fitting RSM Models 286(2) 13.2.1 Three Factor Full Quadratic 286(1) 13.2.2 Multiple Functional Forms 287(1) 13.3 One-shot Response Surface Methods 288(3) 13.4 One-shot RSM Examples 291(7) 13.4.1 Food Science Application 298(1) 13.5 Creating 3D Surface Plots in Excel 298(1) 13.6 Sequential Response Surface Methods 299(5) 13.6.1 Lack of Fit 303(1) 13.7 Origin of RSM Designs and Decision-making 304(6) 13.7.1 Origins of the RSM Experimental Arrays 304(3) 13.7.2 Decision Support Information (Optional) 307(3) 13.8 Appendix: Additional Response Surface Designs 310(5) 13.9 Chapter Summary 315(1) 13.10 References 315(1) 13.11 Problems 316(5) 14 DOE: Robust Design 321(22) 14.1 Introduction 321(2) 14.2 Expected Profits and Control-by-noise Interactions 323(2) 14.2.1 Polynomials in Standard Format 324(1) 14.3 Robust Design Based on Profit Maximization 325(7) 14.3.1 Example of RDPM and Central Composite Designs 326(6) 14.3.2 RDPM and Six Sigma 332(1) 14.4 Extended Taguchi Methods 332(4) 14.4.1 Welding Process Design Example Revisited 334(2) 14.5 Literature Review and Methods Comparison 336(2) 14.6 Chapter Summary 338(1) 14.7 References 338(1) 14.8 Problems 339(4) 15 Regression 343(36) 15.1 Introduction 343(1) 15.2 Single Variable Example 344(2) 15.2.1 Demand Trend Analysis 345(1) 15.2.2 The Least Squares Formula 345(1) 15.3 Preparing "Flat Files" and Missing Data 346(2) 15.3.1 Handling Missing Data 347(1) 15.4 Evaluating Models and DOE Theory 348(11) 15.4.1 Variance Inflation Factors and Correlation Matrices 349(1) 15.4.2 Evaluating Data Quality 350(1) 15.4.3 Normal Probability Plots and Other "Residual Plots" 351(2) 15.4.4 Normal Probability Plotting Residuals 353(3) 15.4.5 Summary Statistics 356(1) 15.4.6 R² Adjusted Calculations 356(1) 15.4.7 Calculating R² Prediction 357(1) 15.4.8 Estimating Sigma Using Regression 358(1) 15.5 Analysis of Variance Followed by Multiple T-tests 359(3) 15.5.1 Single Factor ANOVA Application 361(1) 15.6 Regression Modeling Flowchart 362(5) 15.6.1 Method Choices 363(1) 15.6.2 Body Fat Prediction 364(3) 15.7 Categorical and Mixture Factors (Optional) 367(4) 15.7.1 Regression with Categorical Factors 368(1) 15.7.2 DOE with Categorical Inputs and Outputs 369(1) 15.7.3 Recipe Factors or "Mixture Components" 370(1) 15.7.4 Method Choices 371(1) 15.8 Chapter Summary 371(1) 15.9 References 372(1) 15.10 Problems 372(7) 16 Advanced Regression and Alternatives 379(22) 16.1 Introduction 379(1) 16.2 Generic Curve Fitting 379(2) 16.2.1 Curve Fitting Example 380(1) 16.3 Kriging Model and Computer Experiments 381(4) 16.3.1 Design of Experiments for Kriging Models 382(1) 16.3.2 Fitting Kriging Models 382(3) 16.3.3 Kriging Single Variable Example 385(1) 16.4 Neural Nets for Regression Type Problems 385(6) 16.5 Logistics Regression and Discrete Choice Models 391(6) 16.5.1 Design of Experiments for Logistic Regression 393(1) 16.5.2 Fitting Logit Models 394(1) 16.5.3 Paper Helicopter Logistic Regression Example 395(2) 16.6 Chapter Summary 397(1) 16.7 References 397(1) 16.8 Problems 398(3) 17 DOE and Regression Case Studies 401(22) 17.1 Introduction 401(1) 17.2 Case Study: the Rubber Machine 401(2) 17.2.1 The Situation 401(1) 17.2.2 Background Information 402(1) 17.2.3 The Problem Statement 402(1) 17.3 The Application of Formal Improvement Systems Technology 403(4) 17.4 Case Study: Snap Tab Design Improvement 407(3) 17.5 The Selection of the Factors 410(1) 17.6 General Procedure for Low Cost Response Surface Methods 411(1) 17.7 The Engineering Design of Snap Fits 411(4) 17.8 Concept Review 415(1) 17.9 Additional Discussion of Randomization 416(2) 17.10 Chapter Summary 418(1) 17.11 References 419(1) 17.12 Problems 419(4) 18 DOE and Regression Theory 423(34) 18.1 Introduction 423(1) 18.2 Design of Experiments Criteria 424(1) 18.3 Generating "Pseudo-Random" Numbers 425(7) 18.3.1 Other Distributions 427(2) 18.3.2 Correlated Random Variables 429(1) 18.3.3 Monte Carlo Simulation (Review) 430(1) 18.3.4 The Law of the Unconscious Statistician 431(1) 18.4 Simulating T-testing 432(5) 18.4.1 Sample Size Determination for T-testing 435(2) 18.5 Simulating Standard Screening Methods 437(2) 18.6 Evaluating Response Surface Methods 439(11) 18.6.1 Taylor Series and Reasonable Assumptions 440(1) 18.6.2 Regression and Expected Prediction Errors 441(3) 18.6.3 The EIMSE Formula 444(6) 18.7 Chapter Summary 450(1) 18.8 References 451(1) 18.9 Problems 451(6) Part III Optimization and Strategy 19 Optimization And Strategy 457(22) 19.1 Introduction 457(1) 19.2 Formal Optimization 458(5) 19.2.1 Heuristics and Rigorous Methods 461(2) 19.3 Stochastic Optimization 463(3) 19.4 Genetic Algorithms 466(3) 19.4.1 Genetic Algorithms for Stochastic Optimization 465(1) 19.4.2 Populations, Cross-over, and Mutation 466(1) 19.4.3 An Elitist Genetic Algorithm with Immigration 467(1) 19.4.4 Test Stochastic Optimization Problems 468(1) 19.5 Variants on the Proposed Methods 469(1) 19.6 Appendix: C Code for "Toycoolga" 470(4) 19.7 Chapter Summary 474(1) 19.8 References 474(1) 19.9 Problems 475(4) 20 Tolerance Design 479(4) 20.1 Introduction 479(2) 20.2 Chapter Summary 481(1) 20.3 References 481(1) 20.4 Problems 481(2) 21 Six Sigma Project Design 483(16) 21.1 Introduction 483(1) 21.2 Literature Review 484(1) 21.3 Reverse Engineering Six Sigma 485(2) 21.4 Uncovering and Solving Optimization Problems 487(3) 21.5 Future Research Opportunities 490(5) 21.5.1 New Methods from Stochastic Optimization 491(1) 21.5.2 Meso-Analyses of Project Databases 492(2) 21.5.3 Test Beds and Optimal Strategies 494(1) 21.6 References 495(1) 21.7 Problems 496(3) Glossary 499(6) Problem Solutions 505(18) Index 523