Introduction to Engineering Statistics and Six Sigma

Transcription

1 Theodore T. Allen Introduction to Engineering Statistics and Six Sigma Statistical Quality Control and Design of Experiments and Systems With 114 Figures 4y Spri ringer

2 Contents List of Acronyms xxi 1 Introduction Purpose of this Book Systems and Key Input Variables Problem-solving Methods Whatls "Six Sigma"? History of "Quality" and Six Sigma History of Management and Quality History of Documentation and Quality History of Statistics and Quality The Six Sigma Movement The Culture ofdiscipline Real Success Stories Overview of this Book References Problems 22 Part I Statistical Quality Control 2 Statistical Quality Control and Six Sigma Introduction Method Names as Buzzwords Where Methods Fit into Projects Organizational Roles and Methods Specifications: Nonconforming vs Defective Standard Operating Procedures (SOPs) Proposed SOP Process Measurement SOPs References Problems 41 3 Define Phase and Strategy Introduction 45

3 xiv Contents 3.2 Systems and Subsystems Project Charters Predicting Expected Profits Strategies for Project Definition Bottleneck Subsystems Go-no-go Decisions Methods for Define Phases Pareto Charting Benchmarking Formal Meetings Significant Figures Chapter Summary References Problems 65 4 Measure Phase and Statistical Charting Introduction Evaluating Measurement Systems TypesofGaugeR&R Methods Gauge R&R: Comparison with Standards Gauge R&R (Crossed) with Xbar & R Analysis Measuring Quality Using SPC Charting Concepts: Common Causes and Assignable Causes Commonality: Rational Subgroups, Control Limits, and Startup Attribute Data: ^»-Charting Attribute Data: Demerit Charting and w-charting Continuous Data: Xbar & R Charting Alternative Continuous Data Charting Methods Chapter Summary and Conclusions References Problems Analyze Phase Introduction Process Mapping and Value Stream Mapping The Toyota Production System Cause and Effect Matrices Design of Experiments and Regression (Preview) Failure Mode and Effects Analysis Chapter Summary References Problems Improve or Design Phase Introduction Informal Optimization Quality Function Deployment (QFD) 137

4 Contents xv 6.4 Formal Optimization Chapter Summary References Problems Control or Verify Phase Introduction Control Planning Acceptance Sampling Single Sampling Double Sampling Documenting Results Chapter Summary References Problems Advanced SQC Methods Introduction EWMA Charting for Continuous Data Multivariate Charting Concepts Multivariate Charting (Hotelling's T 2 Charts) Summary References Problems SQC Case Studies Introduction Case Study: Printed Circuit Boards Experience of the First Team Second Team Actions and Results Printed Circuitboard: Analyze, Improve, and Control Phases Wire Harness Voids Study Define Phase Measure Phase Analyze Phase Improve Phase Control Phase Case Study Exercise Project to Improve a Paper Air Wings System Chapter Summary References Problems SQCTheory Introduction Probability Theory Continuous Random Variables 203

5 xvi Contents The Normal Probability Density Function Defects Per Million Opportunities Independent, Identically Distributed and Charting The Central Limit Theorem Advanced Topic: Derivingd 2 andc Discrete Random Variables The Geometrie and Hypergeometric Distributions Xbar Charts and Average Run Length The Chance ofa Signal Average Run Length OC Curves and Average Sample Number Single Sampling OC Curves Double Sampling Double Sampling Average Sample Number Chapter Summary References Problems 234 Part II Design of Experiments (DOE) and Regression 11 DOE: The Jewel of Quality Engineering Introduction Design of Experiments Methods Overview Method Choices The Two-sample T-test Methodology and the Word "Proven" T-test Examples Second T-test Application Randomization and Evidence Poor Randomization and Waste Errors from DOE Procedures Testing anewdrug Chapter Summary Student Retention Study Problems DOE: Screening Using Fractional Factorials Introduction Standard Screening Using Fractional Factorials Screening Examples More Detailed Application Method Origins and Alternatives Origins of the Arrays Experimental Design Generation Alternatives to the Methods in this Chapter Standard vs One-factor-at-a-time Experimentation Printed Circuit Board Related Method Choices 277

6 Contents xvii 12.6 Chapter Summary References Problems 278 DOE: Response Surface Methods Introduction Design Matrices for Fitting RSM Models Three Factor Füll Quadratic Multiple Functional Forms One-shot Response Surface Methods One-shot RSM Examples Food Science Application Creating 3D Surface Plots in Excel Sequential Response Surface Methods Lack of Fit Originof RSM Designs and Decision-making Origins of the RSM Experimental Arrays Decision Support Information (Optional) Appendix: Additional Response Surface Designs Chapter Summary References Problems 316 DOE: Robust Design Introduction Expected Profits and Control-by-noise Interactions Polynomials in Standard Format Robust Design Based on Profit Maximization Example of RDPM and Central Composite Designs RDPM and Six Sigma Extended Taguchi Methods Welding Process Design Example Revisited Literature Review and Methods Comparison Chapter Summary References Problems 339 Regression Introduction Single Variable Example Demand Trend Analysis The Least Squares Formula Preparing "Fiat Files" and Missing Data Handling Missing Data Evaluating Models and DOE Theory Variance Inflation Factors and Correlation Matrices Evaluating Data Quality 350

7 xviii Contents Normal Probability Plots and Other "Residual Plots" Normal Probability Plotting Residuais Summary Statistics R 2 Adjusted Calculations Calculating R 2 Prediction Estimating Sigma Using Regression Analysis of Variance Followed by Multiple T-tests Single Factor ANOVA Application Regression Modeling Flowchart Method Choices Body Fat Prediction Categorical and Mixture Factors (Optional) Regression with Categorical Factors DOE with Categorical Inputs and Outputs Recipe Factors or "Mixture Components" Method Choices Chapter Summary References Problems Advanced Regression and Alternatives Introduction Generic Curve Fitting Curve Fitting Example Kriging Model and Computer Experiments Design of Experiments for Kriging Models Fitting Kriging Models Kriging Single Variable Example Neural Nets for Regression Type Problems Logistics Regression and Discrete Choice Models Design of Experiments for Logistic Regression Fitting Logit Models Paper Helicopter Logistic Regression Example Chapter Summary References Problems DOE and Regression Case Studies Introduction Case Study: the Rubber Machine The Situation Background Information The Problem Statement The Application of Formal Improvement Systems Technology Case Study: Snap Tab Design Improvement The Selection of the Factors General Procedure for Low Cost Response Surface Methods

8 Contents xix 17.7 The Engineering Design of Snap Fits Concept Review Additional Discussion of Randomization Chapter Summary References Problems DOE and Regression Theory Introduction Design of Experiments Criteria Generating "Pseudo-Random" Numbers Other Distributions Correlated Random Variables Monte Carlo Simulation (Review) The Lawof the Unconscious Statistician Simulating T-testing Sample Size Determination for T-testing Simulating Standard Screening Methods Evaluating Response Surface Methods Taylor Series and Reasonable Assumptions Regression and Expected Prediction Errors The EIMSE Formula Chapter Summary References Problems 451 Part III Optimization and Strategy 19 Optimization And Strategy Introduction Formal Optimization Heuristics and Rigorous Methods Stochastic Optimization Genetic Algorithms Genetic Algorithms for Stochastic Optimization Populations, Cross-over, and Mutation An Elitist Genetic Algorithm with Immigration Test Stochastic Optimization Problems Variants onthe Proposed Methods Appendix: C Code for "Toycoolga" Chapter Summary References Problems Tolerance Design Introduction 479

9 xx Contents 20.2 Chapter Summary References Problems Six Sigma Project Design Introduction Literature Review Reverse Engineering Six Sigma Uncovering and Solving Optimization Problems Future Research Opportunities New Methods from Stochastic Optimization Meso-Analyses of Project Databases Test Beds and Optimal Strategies References Problems 496 Glossary 499 Problem Solutions 505 Index 523