Statistical Methods for Quality Improvement

Transcription

1 Statistical Methods for Quality Improvement Third Edition THOMAS P. RYAN Smyrna, Georgia WILEY A JOHN WILEY AND SONS, INC., PUBLICATION

2 Contents Preface Preface to the Second Edition Preface to the First Edition xix xxi xxiii PART I FUNDAMENTAL QUALITY IMPROVEMENT AND STATISTICAL CONCEPTS 1 Introduction Quality and Productivity, Quality Costs (or Does It?), The Need for Statistical Methods, Early Use of Statistical Methods for Improving Quality, Influential Quality Experts, Summary, 9 References, 10 2 Basic Tools for Improving Quality Histogram, Pareto Charts, Scatter Plots, Variations of Scatter Plots, Control Chart, Check Sheet, Cause-and-Effect Diagram, Defect Concentration Diagram, 28

3 VI CONTENTS 2.8 The Seven Newer Tools, Software, Summary, 31 References, 311 Exercises, 32 Affinity Diagram, 28 Interrelationship Digraph, 29 Tree Diagram, 29 Prioritization Matrix, 29 Matrix Diagram, 30 Process Decision Program Chart, 30 Activity Network Diagram, 30 Basic Concepts in Statistics and Probability Probability, Sample 1 Versus Population, 35 Location 36 VariatiorI, 38 Discrete Distributions, Binomial Distribution, Beta-Binomial Distribution, Poisson Distribution, Geometric Distribution, Negative Binomial Distribution, Hypergeometric Distribution, 53 Continuous Distributions, Normal Distribution, 55 t Distribution, 59 Exponential Distribution, 61 Lognormal Distribution, 62 Weibull Distribution, 64 Extreme Value Distribution, 64 Gamma Distribution, 64 Chi-Square Distribution, 65 Truncated Normal Distribution, 65 Bivariate and Multivariate Normal Distributions, 66 F Distribution, 67 Beta Distribution, 68 Uniform Distribution, 68

4 CONTENTS. Vll 3.7 Choice of Statistical Distribution, Statistical Inference, Central Limit Theorem, Point Estimation, Maximum Likelihood Estimation, Confidence Intervals, Tolerance Intervals, Hypothesis Tests, Probability Plots, Likelihood Ratio Tests, Bonferroni Intervals, Enumerative Studies Versus Analytic Studies, 81 References, 81 Exercises, 83 PART II CONTROL CHARTS AND PROCESS CAPABILITY 4 Control Charts for Measurements With Subgrouping (for One Variable) Basic Control Chart Principles, Real-Time Control Charting Versus Analysis of Past Data, Control Charts: When to Use, Where to Use, How Many to Use, Benefits from the Use of Control Charts, Rational Subgroups, Basic Statistical Aspects of Control Charts, Illustrative Example, /?-Chart, K-Chart with Probability Limits, S-Chart, Chart with Probability Limits, S 2 -Chart, X-Chart, Recomputing Control Limits, Applying Control Limits to Future Production, Combining an X-and an S-Chart, Standards for Control Charts, Deleting Points, Target Values, 114

5 Vlll. CONTENTS 4.8 Illustrative Example with Real Data, Determining the Point of a Parameter Change, Acceptance Sampling and Acceptance Control Chart, Acceptance Control Chart, Acceptance Chart with X Control Limits, Acceptance Charts Versus Target Values, Modified Limits, Difference Control Charts, Other Charts, Average Run Length (ARL), Weakness of the ARL Measure, Determining the Subgroup Size, Unequal Subgroup Sizes, Out-of-Control Action Plans, Assumptions for the Charts in This Chapter, Normality, Independence, Measurement Error, Monitoring Measurement Systems, Software, Summary, 143 Appendix, A Derivation of Control Chart Constants, B ARL Calculations, 146 References, 146 Exercises, Control Charts for Measurements Without Subgrouping (for One Variable) Individual Observations Chart, Control Limits for the X-Chart, X-Chart Assumptions, Illustrative Example: Random Data, Example with Particle Counts, Illustrative Example: Trended Data, Trended Real Data, Transform the Data or Fit a Distribution?, Moving Average Chart, 171

6 CONTENTS IX 5.4 Controlling Variability with Individual Observations, Summary, 175 Appendix, 176 References, 176 Exercises, Control Charts for Attributes Charts for Nonconforming Units, np-chart, p-chart, Stage 1 and Stage 2 Use of p-charts and np-charts, Alternative Approaches, Arcsin Transformations, Q-Chart for Binomial Data, Regression-Based Limits, ARL-Unbiased Charts, Unit and Group-Runs Chart, Monitoring a Multinomial Process, Using Software to Obtain Probability Limits for p- and np-charts, Variable Sample Size, Charts Based on the Geometric and Negative Binomial Distributions, Overdispersion, Charts for Nonconformities, c-chart, Transforming Poisson Data, Illustrative Example, Regression-Based Limits, Using Software to Obtain Probability Limits for c-charts, M-Chart, Regression-Based Limits, Using Computer Software to Obtain w-chart Probability Limits, Overdispersion, D-Chart, Probability-Type D-Chart Limits, Summary, 218

7 X CONTENTS References, 218 Exercises, Process Capability Data Acquisition for Capability Indices, Selection of Historical Data, Process Capability Indices, C p, C pm, C pk, CPU and CPL as Process Capability Indices, C pmk, Other Capability Indices, Estimating the Parameters in Process Capability Indices, X-Chart, X-Chart, Case Study, Distributional Assumption for Capability Indices, Confidence Intervals for Process Capability Indices, Confidence Interval for C p, Confidence Interval for C p t, Confidence Interval for C pm, Confidence Interval for C /w,,<, Confidence Intervals Computed Using Data in Subgroups, Nonparametric Capability Indices and Confidence Limits, Robust Capability Indices, Capability Indices Based on Fitted Distributions, Data Transformation, Capability Indices Computed Using Resampling Methods, Asymmetric Bilateral Tolerances, Examples, Capability Indices That Are a Function of Percent Nonconforming, Examples, Modified k Index, Other Approaches, Process Capability Plots, 251

8 CONTENTS XI 7.11 Process Capability Indices Versus Process Performance Indices, Process Capability Indices with Autocorrelated Data, Software for Process Capability Indices, Summary, 253 References, 254 Exercises, Alternatives to Shewhart Charts Introduction, Cumulative Sum Procedures: Principles and Historical Development, CUSUM Procedures Versus X-Chart, Fast Initial Response CUSUM, Combined Shewhart-CUSUM Scheme, CUSUMs with Estimated Parameters, Computation of CUSUM ARLs, Robustness of CUSUM Procedures, CUSUM Procedures for Individual Observations, CUSUM Procedures for Controlling Process Variability, Applications of CUSUM Procedures, Generalized Likelihood Ratio Charts: Competitive Alternative to CUSUM Charts, CUSUM Procedures for Nonconforming Units, CUSUM Procedures for Nonconformity Data, Exponentially Weighted Moving/Average Charts, EWMA Chart for Subgroup Averages, EWMA Misconceptions, EWMA Chart for Individual Observations, Shewhart-EWMA Chart, FIR-EWMA, Designing EWMA Charts with Estimated Parameters, EWMA Chart with Variable Sampling Intervals, EWMA Chart for Grouped Data, EWMA Chart for Variances, EWMA for Attribute Data, Software, Summary, 301 References, 301 Exercises, 306

9 XU CONTENTS 9 Multivariate Control Charts for Measurement and Attribute Data Hotelling's T 2 Distribution, A T 2 Control Chart, Robust Parameter Estimation, Identifying the Sources of the Signal, Regression Adjustment, Recomputing the UCL, Characteristics of Control Charts Based on T 2, Determination of a Change in the Correlation Structure, Illustrative Example, Multivariate Chart Versus Individual X-Charts, Charts for Detecting Variability and Correlation Shifts, Application to Table 9.2 Data, Charts Constructed Using Individual Observations, Retrospective (Stage 1) Analysis, Stage 2 Analysis: Methods for Decomposing Q, Illustrative Example, Other Methods, Monitoring Multivariate Variability with Individual Observations, When to Use Each Chart, Actual Alpha Levels for Multiple Points, Requisite Assumptions, Effects of Parameter Estimation on ARLs, Dimension-Reduction and Variable Selection Techniques, Multivariate CUSUM Charts, Multivariate EWMA Charts, Design of a MEWMA Chart, Searching for Assignable Causes, Unequal Sample Sizes, Self-Starting MEWMA Chart, Combinations of MEWMA Charts and Multivariate Shewhart Charts, MEWMA Chart with Sequential Sampling, MEWMA Chart for Process Variability, Effect of Measurement Error, Applications of Multivariate Charts, Multivariate Process Capability Indices, 344

10 CONTENTS Xlll 9.16 Summary, 344 Appendix, 345 References, 345 Exercises, Miscellaneous Control Chart Topics Pre-control, Short-Run SPC, Charts for Autocorrelated Data, Autocorrelated Attribute Data, Charts for Batch Processes, Charts for Multiple-Stream Processes, Nonparametric Control Charts, Bayesian Control Chart Methods, Control Charts for Variance Components, Control Charts for Highly Censored Data, Neural Networks, Economic Design of Control Charts, Economic-Statistical Design, Charts with Variable Sample Size and/or Variable Sampling Interval, Users of Control Charts, Control Chart Nonmanufacturing Applications, HealthCare, Financial, Environmental, Clinical Laboratories, Analytical Laboratories, Civil Engineering, Education, Law Enforcement/Investigative Work, Lumber, Forest Operations, Athletic Performance, Animal Production Systems, Software for Control Charting, 374 Bibliography, 375 Exercises, 384

11 XIV CONTENTS PART III BEYOND CONTROL CHARTS: GRAPHICAL AND STATISTICAL METHODS 11 Graphical Methods Histogram, Stem-and-Leaf Display, Dot Diagrams, DigidotPlot, Boxplot, Normal Probability Plot, Plotting Three Variables, Displaying More Than Three Variables, Plots to Aid in Transforming Data, Summary, 401 References, 402 Exercises, Linear Regression Simple Linear Regression, Worth of the Prediction Equation, Assumptions, Checking Assumptions Through Residual Plots, Confidence Intervals and Hypothesis Test, Prediction Interval for Y, Regression Control Chart, Cause-Selecting Control Charts, Linear, Nonlinear, and Nonparametric Profiles, Inverse Regression, Multiple Linear Regression, Issues in Multiple Regression, Variable Selection, Extrapolation, Multicollinear Data, Residual Plots, Regression Diagnostics, Transformations, Software For Regression, Summary, 429

12 CONTENTS XV References, 430 Exercises, Design of Experiments A Simple Example of Experimental Design Principles, Principles of Experimental Design, Statistical Concepts in Experimental Design, f-tests, Exact *-Test, Approximate t-test, Confidence Intervals for Differences, Analysis of Variance for One Factor, ANOVA for a Single Factor with More Than Two Levels, Multiple Comparison Procedures, Sample Size Determination, Additional Terms and Concepts in One-Factor ANOVA, Regression Analysis of Data from Designed Experiments, ANOVA for Two Factors, ANOVA with Two Factors: Factorial Designs, Conditional Effects, Effect Estimates, ANOVA Table for Unreplicated Two-Factor Design, Yates's Algorithm, The 2 3 Design, Assessment of Effects Without a Residual Term, Residual Plot, Separate Analyses Using Design Units and Uncoded Units, Two-Level Designs with More Than Three Factors, Three-Level Factorial Designs, Mixed Factorials, Fractional Factorials, *"' Designs, k - 2 Designs, More Highly Fractionated Two-Level Designs, Fractions of Three-Level Factorials, Incomplete Mixed Factorials, Cautions, 493

13 XVI CONTENTS Other Topics in Experimental Design and Their Applications, Hard-to-Change Factors, Split-Lot Designs, Mixture Designs, Response Surface Designs, Designs for Measurement System Evaluation, Fraction or Design Space Plots, Computer-Aided Design and Expert Systems, Sequential Experimentation, Supersaturated Designs and Analyses, Multiple Responses, Summary, 500 References, 500 Exercises, Contributions of Genichi Taguchi and Alternative Approaches "Taguchi Methods", Quality Engineering, Loss Functions, Distribution Not Centered at the Target, Loss Functions and Specification Limits, Asymmetric Loss Functions, Signal-to-Noise Ratios and Alternatives, Experimental Designs for Stage One, Taguchi Methods of Design, Inner Arrays and Outer Arrays, Orthogonal Arrays as Fractional Factorials, Other Orthogonal Arrays Versus Fractional Factorials, Product Arrays Versus Combined Arrays, Application of Product Array, Cautions, Desirable Robust Designs and Analyses, Designs, Analyses, Experiment to Compare Product Array and Combined Array, Determining Optimum Conditions, 553

14 CONTENTS XV Summary, 558 References, 560 Exercises, Evolutionary Operation EVOP Illustrations, Three Variables, Simplex EVOP, Other EVOP Procedures, Miscellaneous Uses of EVOP, Summary, 582 Appendix, A Derivation of Formula for Estimating cr, 582 References, 583 Exercises, Analysis of Means ANOM for One-Way Classifications, ANOM for Attribute Data, Proportions, Count Data, ANOM When Standards Are Given, Nonconforming Units, Nonconformities, Measurement Data, ANOM for Factorial Designs, Assumptions, An Alternative Way of Displaying Interaction Effects, ANOM When at Least One Factor Has More Than Two Levels, Main Effects, Interaction Effects, Use of ANOM with Other Designs, Nonparametric ANOM, 610 v 16.8 Summary, 611 Appendix, 611 References, 611 Exercises, 613

15 XV111 CONTENTS 17 Using Combinations of Quality Improvement Tools Control Charts and Design of Experiments, Control Charts and Calibration Experiments, Six Sigma Programs, Components of a Six Sigma Program, Six Sigma Applications and Programs, Six Sigma Concept for Customer Satisfaction, Six Sigma Training, Lean Six Sigma, Related Programs/Other Companies, SEMATECH's Qual Plan, AlliedSignaPs Operational Excellence Program, Statistical Process Control and Engineering Process Control, 624 References, 625 Answers to Selected Exercises 629 Appendix: Statistical Tables 633 Author Index 645 Subject Index 657