Design of Experiments A Modern Approach

Design of Experiments: A Modern Approach introduces readers to planning and conducting experiments, analyzing the resulting data, and obtaining valid and objective conclusions. This innovative textbook uses design optimization as its design construction approach, focusing on practical experiments in engineering, science, and business rather than orthogonal designs and extensive analysis. Requiring only first-course knowledge of statistics and familiarity with matrix algebra, student-friendly chapters cover the design process for a range of various types of experiments.

The text follows a traditional outline for a design of experiments course, beginning with an introduction to the topic, historical notes, a review of fundamental statistics concepts, and a systematic process for designing and conducting experiments. Subsequent chapters cover simple comparative experiments, variance analysis, two-factor factorial experiments, randomized complete block design, response surface methodology, designs for nonlinear models, and more. Readers gain a solid understanding of the role of experimentation in technology commercialization and product realization activities—including new product design, manufacturing process development, and process improvement—as well as many applications of designed experiments in other areas such as marketing, service operations, e-commerce, and general business operations.

Student Solution Available in Interactive e-Text

Preface iii

About the Authors v

1 Experimental Design: Principles and Practices and Statistics Review 1

1.1 The Strategy of Experimentation 1

1.2 Basic Principles 8

1.3 Practical Guidelines for Designing an Experiment 10

1.3.1 Recognition of and Statement of the Problem 10

1.3.2 Selection of the Response Variable 11

1.3.3 Choice of Factors, Levels, and Ranges 11

1.3.4 Experimental Design Generation 13

1.3.5 Performing the Experiment 14

1.3.6 Statistical Analysis of the Data 14

1.3.7 Conclusions and Recommendations 15

1.4 A Brief History of Designed Experiments 15

1.5 A Review: Using Statistical Techniques in Experimentation 17

1.6 Review of Some Basic Statistical Concepts and Methods 18

1.6.1 Data Description 18

1.6.2 Random Samples, Statistics and Sampling Distributions 23

1.6.3 Statistical Intervals and Tests of Hypotheses 28

2 Simple Comparative Experiments 42

2.1 Introduction 42

2.2 Statistical Methods for Comparing Two Population Means 42

2.2.1 Parameter Estimation and Confidence Intervals 42

2.2.2 Statistical Hypothesis Testing on the Difference in Means 47

2.3 Comparison of Two Means, Variances Unknown 51

2.3.1 Confidence Intervals on the Difference in Means of Two Normal Distributions, Variances Unknown 52

2.3.2 Hypothesis Testing on the Difference in Means of Two Normal Distributions with Unknown Variances 54

2.3.3 Comparison of Means of Two Normal Distributions with Variances Unknown but Assumed Equal 56

2.3.4 Power and Sample Size Calculations 57

2.3.5 The Normality Assumption 57

3 Experiments With a Single Categorical Factor: Design Issues and the Analysis of Variance 59

3.1 Motivating Example 59

3.2 Statistical Model for the Data 61

3.3 Design Considerations 62

3.4 Statistical Analysis of the Data 62

3.4.1 Partitioning the Variance of the Response 63

3.4.2 The ANOVA 64

3.4.3 Post-ANOVA Comparison of Treatment Means 65

3.4.4 Comparing Treatment Means with a Control 68

3.4.5 The Effects Model 70

3.5 Model Adequacy Checking 71

3.5.1 Checking the Normality Assumption 71

3.5.2 Checking for Nonconstant Variance 73

3.6 Power and Sample Size 75

4 Experiments With a Single Continuous Factor: Design Issues and the Regression Analysis 77

4.1 Motivating Example 77

4.2 Statistical Models for the Data 77

4.3 Fitting a Statistical Model Using the Data 79

4.4 Design Considerations 82

4.5 Design Comparison 83

5 Two-Factor Factorial Experiments 87

5.1 Basic Concepts 87

5.2 Two Categorical Factors 89

5.3 The Analysis of Variance for a Two-factor Factorial 92

5.4 One Categorical Factor and One Continuous Factor 98

5.5 Two Continuous Factors 100

5.6 Design and Analysis When Some Factor Level Combinations Are Infeasible 105

6 Blocking 109

6.1 The Randomized Complete Block Design 109

6.2 Statistical Analysis of the RCBD 110

6.3 Blocking and Optimal Designs 113

7 The 2^k Factorial Design 118

7.1 Introduction 118

7.2 The 2² Factorial Design 118

7.2.1 How Much Replication is Necessary? 119

7.3 The 2³ Factorial Design 123

7.3.1 Replication of the 2³ Design 128

7.4 A Single Replicate of the 2^k Design 129

7.5 2^k Designs are Optimal Designs 133

7.6 More About Replication of 2^k Designs 135

7.6.1 Adding Center Runs to a 2^k Design 137

7.7 Blocking in 2^k Designs 138

8 Screening Experiments 140

8.1 Introduction 140

8.2 Regular Fractional Factorial Designs for Factor Screening 141

8.2.1 A General Method for Finding the Alias Relationships in Fractional Factorial Designs 144

8.2.2 Dealiasing Effects 148

8.3 Nonregular Orthogonal Designs 150

8.4 Nonorthogonal Screening Designs 153

8.5 Definitive Screening Designs 156

8.5.1 Statistical Properties of a DSD 158

8.5.2 Constructing DSDs Using Conference Matrices 158

8.5.3 Constructing DSDs with Additional Two-level Categorical Factors 159

8.5.4 Constructing Orthogonally Blocked DSDs 159

8.5.5 Situations When You Should Use a Screening Design Other Than a DSD 159

8.5.6 Recommendations 160

8.6 Screening Summary 160

9 Experiments With Random Blocks 163

9.1 Introduction 163

9.2 Motivating Example: Design and Analysis 164

9.3 Matrix Formulation of the Model for an Experiment with Random Blocks 165

9.4 Design Considerations 166

9.5 A Screening Design with a Random Blocking Factor 166

9.6 Recommendations for Use of Designs with Random Blocks 170

10 Split-Plot Experiments 172

10.1 Introduction 172

10.2 Motivating Example: Design and Analysis 173

10.3 Matrix Formulation of the Model for a Split-plot Experiment 174

10.4 Design Considerations 176

10.5 Split-plot Screening Design 176

10.6 Recommendations for Use of Split-plot Designs 177

11 Response Surface Methods 180

11.1 Introduction 180

11.2 Optimization Techniques in RSM 182

11.3 Response Surface Designs 196

11.3.1 Classical Response Surface Designs 196

11.3.2 Definitive Screening Designs 197

11.3.3 Optimal Designs in RSM 201

12 Design For Models That are Nonlinear in the Parameters 203

12.1 Introduction 203

12.2 Design and Analysis of Exponential Decay 204

12.3 Analysis and Locally Optimal Design of the Michaelis–Menten Model 206

12.4 Yield Optimization as a Function of Reaction Temperature and Time 207

12.5 Mathematical Details for Constructing Optimal Designs for Nonlinear Models 208

12.6 Optimal Design for Situations Where the Response is Binary 210

12.7 Multifactor Binomial Model Experiments 212

12.8 Mathematical Details for Constructing Optimal Designs for Generalized Linear Models 213

Problems P-1

A JMP Scripting Commands For Computing Distribution Probabilities and Quantiles A-1

References R-1

Index I-1

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.