DESIGN AND ANALYSIS OF EXPERIMENTS Third Edition

Transcription

1 DESIGN AND ANALYSIS OF EXPERIMENTS Third Edition Douglas C. Montgomery ARIZONA STATE UNIVERSITY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore

2 Contents Chapter 1. Introduction 1-1 What Is Experimental Design? 1-2 Applications of Experimental Design 1-3 Basic Principles 1-4 Guidelines for Designing Experiments 1-5 Historical Perspective 1-6 Using Statistical Techniques in Experimentation Chapter 2. Simple Comparative Experiments 2-1 Introduction 2-2 Basic Statistical Concepts 2-3 Sampling and Sampling Distributions Inferences About the Differences in Means, Randomized 2-5 I Designs Hypothesis Testing Choice of Sample Size Confidence Intervals 1 r The Case Where a\ and a\ Are Known Comparing a Single Mean to a Specified Value Summary nferences About the Difference in Means, Paired Comparison Designs The Paired Comparison Problem Advantages of the Paired Comparison Design Inferences About the Variances of Normal Distributions u

3 XÜ Contents Chapter 3. Experiments with a Single Factor: The Analysis of Variance 3-1 An Example 3-2 The Analysis of Variance 3-3 Analysis of the Fixed Effects Model Decomposition of the Total Sum of Squares Statistical Analysis Estimation of the Model Parameters Model Adequacy Checking: Preview The Unbalanced Case 3-4 Comparison of Individual Treatment Means Graphical Comparison of Means Contrasts Orthogonal Contrasts Scheffe's Method for Comparing All Contrasts Comparing Pairs of Treatment Means Comparing Treatments with a Control 3-5 The Random Effects Model 3-6 Sample Computer Output Chapter 4. More About Single-Factor Experiments Model Adequacy Checking The Normality Assumption Plot of Residuais in Time Sequence Plot of Residuais Versus Fitted Values y Selecting a Variance-Stabilizing Transformation Plots of Residuais Versus Other Variables Discovering Dispersion Effects Choice of Sample Size Operating Characteristic Curves Specifying a Standard Deviation Increase Confidence Interval Estimation Method Fitting Response Curves in the Single-Factor One-Way Model General Regression Approach Orthogonal Polynomials The Regression Approach to the Analysis of Variance Nonparametric Methods in the Analysis of Variance The Kruskal-Wallis Test General Comments on the Rank Transformation Repeated Measures

4 Contents XÜi Chapter 5. Randomized Blocks, Latin Squares, and Related Designs The Randomized Complete Block Design Statistical Analysis Model Adequacy Checking Estimating Missing Values Estimating Model Parameters and the General Regression Significance Test Sample Computer Output The Latin Square Design The Graeco-Latin Square Design Chapter Incomplete Block Designs 176 Introduction 176 Balanced Incomplete Block Designs Statistical Analysis Least Squares Estimation of the Parameters 183 Recovery of Interblock Information in the Balanced Incomplete Block Design 184 Partially Balanced Incomplete Block Designs 187 Youden Squares 190 Lattice Designs Chapter 7. Introduction to Factorial Designs Basic Definitions and Principles The Advantage of Factorials The Two-Factor Factorial Design An Example Statistical Analysis of the Fixed Effects Model Model Adequacy Checking Estimating the Model Parameters Choice of Sample Size The Assumption of No Interaction in a Two-Factor Model One Observation per Cell 218 Random and Mixed Models The Random Effects Model Mixed Models Choice of Sample Size 228 The General Factorial Design 228 Fitting Response Curves and Surfaces 237 Dealing with Unbalanced Data 244

5 XIV Contents Proportional Data: An Easy Case Approximate Methods The Exact Method Chapter 8. Ruies for Sums of Squares and Expected Mean Squares Chapter Chapter Chapter Chapter Ruies for Sums of Squares Ruies for Expected Mean Squares Approximate F Tests The 2 k Factorial Design Introduction The 2 2 Design The 2 3 Design The General 2 k Design A Single Replicate of the 2 k Design The Addition of Center Points to the 2 k Design Yates' Algorithm for the 2 k Design Confounding in the 2 k Factorial Introduction The 2 k Factorial Design in Two Blocks The 2 k Factorial Design in Four Blocks The 2 k Factorial Design in 2 P Blocks Partial Confounding Two-Level Fractional Factorial Designs Introduction The One-Half Fraction of the 2 k Design The One-Quarter Fraction of the 2 k Design The General 2 k ~ p Fractional Factorial Design Resolution III Designs Resolution IV and V Designs Summary Some Other Topics Regarding Factorial and Fractional Factorial Designs The 3^ Factorial Design Notation and Motivation for the 3 k Design

6 Chapter The 3 2 Design The 3 3 Design The General 3 k Design Yates' Algorithm for the 3 k Design Confounding in the 3 k Factorial Design The 3 k Factorial Design in Three Blocks The 3 k Factorial Design in Nine Blocks The 3 k Factorial Design in 3 P Blocks Fractional Replication of the 3 k Factorial Design The One-Third Fraction of the 3 k Design Other 3 k ~ p Fractional Factorial Designs Factorials with Mixed Levels 1.1 Factors at Two and Three Levels 1.2 Factors at Two and Four Levels Taguchi's Contributions to Experimental Design and Quality Engineering The Taguchi Philosophy The Taguchi Approach to Parameter Design Nested or Hierarchial Designs Introduction The Two-Stage Nested Design Statistical Analysis Diagnostic Checking Estimation of the Model Parameters The General m-stage Nested Design Designs with Nested and Crossed Factors Contents XV Chapter 14. Multifactor Experiments with Randomization Restrictions Randomized Blocks and latin Squares as Multifactor Designs The Split-Plot Design The Split Split-Plot Design Chapter 15. Regression Analysis 15-1 Introduction 15-2 Simple Linear Regression 15-3 Hypothesis Testing in Simple Linear Regression 15-4 Interval Estimation in Simple Linear Regression 15-5 Model Adequacy Checking

7 XVi Contents Residual Analysis The Lack-of-Fit Test The Coefficient of Determination 15-6 Multiple Linear Regression 15-7 Hypothesis Testing in Multiple Linear Regression 15-8 Other Linear Regression Models 15-9 Sample Computer Printout Chapter Chapter Response Surface Methods and Designs 521 Introduction to Response Surface Methodology 521 The Method of Steepest Ascent 523 Analysis of a Second-Order Model Location of the Stationary Point Characterizing the Response Surface Ridge Systems 538 Experimental Designs for Fitting Response Surfaces Designs for Fitting the First-Order Model Designs for Fitting the Second-Order Model Blocking in Response Surface Designs 548 Mixture Experiments 551 Evolutionary Operation Analysis of Covariance 569 Introduction 569 A Single-Factor Design with One Covariate 569 Development by the General Regression Significance Test 581 Other Covariance Models Bibliography 590 Appendix Table I. Table II. Table III. Table IV. Table V. Table VI. Cumulative Standard Normal Distribution Percentage Points of the t Distribution Percentage Points of the x 2 Distribution Percentage Points of the F Distribution Operating Characteristic Curves for the Fixed Effects Model Analysis of Variance Operating Characteristic Curves for the Random Effects Model Analysis of Variance

8 Contents XVÜ Table VII. Significant Ranges for Duncan's Multiple Range Test 615 Table VIII. Percentage Points of the Studentized Range Statistic 617 Table IX. Critical Values for Dunnett's Test for Comparing Treatments with a Control 619 Table X. Coefficients of Orthogonal Polynomials 623 Table XI. Random Numbers 624 Table XII. Alias Relationships for 2 k ~ p Fractional Factorial Designs with k < 11 and n < Index 645