Design and analysis of experiments

Description

Cover Title Page Copyright Preface Contents Chapter 1: Introduction 1.1 Strategy of Experimentation 1.2 Some Typical Applications of Experimental Design 1.3 Basic Principles 1.4 Guidelines for Designing Experiments 1.5 A Brief History of Statistical Design 1.6 Summary: Using Statistical Techniques in Experimentation 1.7 Problems Chapter 2: Simple Comparative Experiments 2.1 Introduction 2.2 Basic Statistical Concepts 2.3 Sampling and Sampling Distributions 2.4 Inferences About the Differences in Means, Randomized Designs 2.4.1 Hypothesis Testing 2.4.2 Confidence Intervals 2.4.3 Choice of Sample Size 2.4.4 The Case Where 𝝈21 ≠  𝝈22 2.4.5 The Case Where 𝝈21 and 𝝈22 Are Known 2.4.6 Comparing a Single Mean to a Specified Value 2.4.7 Summary 2.5 Inferences About the Differences in Means, Paired Comparison Designs 2.5.1 The Paired Comparison Problem 2.5.2 Advantages of the Paired Comparison Design 2.6 Inferences About the Variances of Normal Distributions 2.7 Problems 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 3.3.1 Decomposition of the Total Sum of Squares 3.3.2 Statistical Analysis 3.3.3 Estimation of the Model Parameters 3.3.4 Unbalanced Data 3.4 Model Adequacy Checking 3.4.1 The Normality Assumption 3.4.2 Plot of Residuals in Time Sequence 3.4.3 Plot of Residuals Versus Fitted Values 3.4.4 Plots of Residuals Versus Other Variables 3.5 Practical Interpretation of Results 3.5.1 A Regression Model 3.5.2 Comparisons Among Treatment Means 3.5.3 Graphical Comparisons of Means 3.5.4 Contrasts 3.5.5 Orthogonal Contrasts 3.5.6 Scheff's Method for Comparing All Contrasts 3.5.7 Comparing Pairs of Treatment Means 3.5.8 Comparing Treatment Means with a Control 3.6 Sample Computer Output 3.7 Determining Sample Size 3.7.1 Operating Characteristic and Power Curves 3.7.2 Confidence Interval Estimation Method 3.8 Other Examples of Single-Factor Experiments 3.8.1 Chocolate and Cardiovascular Health 3.8.2 A Real Economy Application of a Designed Experiment 3.8.3 Discovering Dispersion Effects 3.9 The Random Effects Model 3.9.1 A Single Random Factor 3.9.2 Analysis of Variance for the Random Model 3.9.3 Estimating the Model Parameters 3.10 The Regression Approach to the Analysis of Variance 3.10.1 Least Squares Estimation of the Model Parameters 3.10.2 The General Regression Significance Test 3.11 Nonparametric Methods in the Analysis of Variance 3.11.1 The Kruskal-Wallis Test 3.11.2 General Comments on the Rank Transformation 3.12 Problems Chapter 4: Randomized Blocks, Latin Squares, and Related Designs 4.1 The Randomized Complete Block Design 4.1.1 Statistical Analysis of the RCBD 4.1.2 Model Adequacy Checking 4.1.3 Some Other Aspects of the Randomized Complete Block Design 4.1.4 Estimating Model Parameters and the General Regression Significance Test 4.2 The Latin Square Design 4.3 The Graeco-Latin Square Design 4.4 Balanced Incomplete Block Designs 4.4.1 Statistical Analysis of the BIBD 4.4.2 Least Squares Estimation of the Parameters 4.4.3 Recovery of Interblock Information in the BIBD 4.5 Problems Chapter 5: Introduction to Factorial Designs 5.1 Basic Definitions and Principles 5.2 The Advantage of Factorials 5.3 The Two-Factor Factorial Design 5.3.1 An Example 5.3.2 Statistical Analysis of the Fixed Effects Model 5.3.3 Model Adequacy Checking 5.3.4 Estimating the Model Parameters 5.3.5 Choice of Sample Size 5.3.6 The Assumption of No Interaction in a Two-Factor Model 5.3.7 One Observation per Cell 5.4 The General Factorial Design 5.5 Fitting Response Curves and Surfaces 5.6 Blocking in a Factorial Design 5.7 Problems Chapter 6: The 2k Factorial Design 6.1 Introduction 6.2 The 22 Design 6.3 The 23 Design 6.4 The General 2k Design 6.5 A Single Replicate of the 2k Design 6.6 Additional Examples of Unreplicated 2k Designs 6.7 2k Designs are Optimal Designs 6.8 The Addition of Center Points to the 2k Design 6.9 Why We Work with Coded Design Variables 6.10 Problems Chapter 7: Blocking and Confounding in the 2k Factorial Design 7.1 Introduction 7.2 Blocking a Replicated 2k Factorial Design 7.3 Confounding in the 2k Factorial Design 7.4 Confounding the 2k Factorial Design in Two Blocks 7.5 Another Illustration of Why Blocking Is Important 7.6 Confounding the 2k Factorial Design in Four Blocks 7.7 Confounding the 2k Factorial Design in 2p Blocks 7.8 Partial Confounding 7.9 Problems Chapter 8: Two-Level Fractional Factorial Designs 8.1 Introduction 8.2 The One-Half Fraction of the 2k Design 8.2.1 Definitions and Basic Principles 8.2.2 Design Resolution 8.2.3 Construction and Analysis of the One-Half Fraction 8.3 The One-Quarter Fraction of the 2k Design 8.4 The General 2k-p Fractional Factorial Design 8.4.1 Choosing a Design 8.4.2 Analysis of 2k-p Fractional Factorials 8.4.3 Blocking Fractional Factorials 8.5 Alias Structures in Fractional Factorials and Other Designs 8.6 Resolution III Designs 8.6.1 Constructing Resolution III Designs 8.6.2 Fold Over of Resolution III Fractions to Separate Aliased Effects 8.6.3 Plackett-Burman Designs 8.7 Resolution IV and V Designs 8.7.1 Resolution IV Designs 8.7.2 Sequential Experimentation with Resolution IV Designs 8.7.3 Resolution V Designs 8.8 Supersaturated Designs 8.9 Summary 8.10 Problems Chapter 9: Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs 9.1 The 3k Factorial Design 9.1.1 Notation and Motivation for the 3k Design 9.1.2 The 32 Design 9.1.3 The 33 Design 9.1.4 The General 3k Design 9.2 Confounding in the 3k Factorial Design 9.2.1 The 3k Factorial Design in Three Blocks 9.2.2 The 3k Factorial Design in Nine Blocks 9.2.3 The 3k Factorial Design in 3p Blocks 9.3 Fractional Replication of the 3k Factorial Design 9.3.1 The One-Third Fraction of the 3k Factorial Design 9.3.2 Other 3k-p Fractional Factorial Designs 9.4 Factorials with Mixed Levels 9.4.1 Factors at Two and Three Levels 9.4.2 Factors at Two and Four Levels 9.5 Nonregular Fractional Factorial Designs 9.5.1 Nonregular Fractional Factorial Designs for 6, 7, and 8 Factors in 16 Runs 9.5.2 Nonregular Fractional Factorial Designs for 9 Through 14 Factors in 16 Runs 9.5.3 Analysis of Nonregular Fractional Factorial Designs 9.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool 9.6.1 Design Optimality Criterion 9.6.2 Examples of Optimal Designs 9.6.3 Extensions of the Optimal Design Approach 9.7 Problems Chapter 11: Response Surface Methods and Designs 11.1 Introduction to Response Surface Methodology 11.2 The Method of Steepest Ascent 11.3 Analysis of a Second-Order Response Surface 11.3.1 Location of the Stationary Point 11.3.2 Characterizing the Response Surface 11.3.3 Ridge Systems 11.3.4 Multiple Responses 11.4 Experimental Designs for Fitting Response Surfaces 11.4.1 Designs for Fitting the First-Order Model 11.4.2 Designs for Fitting the Second-Order Model 11.4.3 Blocking in Response Surface Designs 11.4.4 Optimal Designs for Response Surfaces 11.5 Experiments with Computer Models 11.6 Mixture Experiments 11.7 Evolutionary Operation 11.8 Problems Chapter 13: Experiments with Random Factors 13.1 Random Effects Models 13.2 The Two-Factor Factorial with Random Factors 13.3 The Two-Factor Mixed Model 13.4 Rules for Expected Mean Squares 13.5 Approximate F-Tests 13.6 Some Additional Topics on Estimation of Variance Components 13.6.1 Approximate Confidence Intervals on Variance Components 13.6.2 The Modified Large-Sample Method 13.7 Problems Chapter 14: Nested and Split-Plot Designs 14.1 The Two-Stage Nested Design 14.1.1 Statistical Analysis 14.1.2 Diagnostic Checking 14.1.3 Variance Components 14.1.4 Staggered Nested Designs 14.2 The General m-Stage Nested Design 14.3 Designs with Both Nested and Factorial Factors 14.4 The Split-Plot Design 14.5 Other Variations of the Split-Plot Design 14.5.1 Split-Plot Designs with More Than Two Factors 14.5.2 The Split-Split-Plot Design 14.5.3 The Strip-Split-Plot Design 14.6 Problems Index EULA