Table of Contents
1 Introduction 1
1.1 What Is Experimental Design? 1
1.2 Applications of Experimental Design 2
1.3 Old Philosophy of Quality 3
1.4 New Philosophy of Quality 4
1.5 Robust Design 6
1.6 Experimentation Steps 7
1.7 Goals and Outline of the Design of Experiments Concepts 9
1.8 Problems 9
References 10
2 Designing and Conducting the Experiment 13
2.1 Introduction 13
2.2 One-Factor-at-a-Time Approach 13
2.3 Two-Level Factorial Designs 16
A Two-Level Full Factorial Designs 17
B Fractional Factorial Designs of Resolution III 25
C Plackett-Burman (PB) Designs 31
D Fractional Factorial Designs of Resolution IV 36
E Fractional Factorial Designs of Resolution V 44
2.4 Problems 52
References 52
3 Optimization of the Location Parameter 55
3.1 Introduction 55
3.2 Guidelines for Location Optimization 56
3.3 Replicated Experimental Runs 57
A Maximizing the Location Parameter 57
B Prediction 61
C Hit a Target 62
3.4 An Alternative Approach to the Pareto Chart 67
3.5 Problems 78
References 80
4 Minimization of the Dispersion 81
4.1 Introduction 81
4.2 Dispersion Minimization for Replicated Study 83
4.3 Dispersion Minimization for Unreplicated Study 89
4.4 Problems 96
References 96
5 Taguchi's Approach to the Design of Experiments 97
5.1 Introduction 97
5.2 Loss Function 98
5.3 Taguchi Designs 99
5.4 Signal-to-Noise Ratio 101
A Nominal-Is-the-Best 101
B Large-Is-the-Best 103
C Small-Is-the-Best 104
5.5 Applications of Taguchi's Approach to Robust Designs 106
A Analysis: Large-Is-the-Best 106
B Analysis: Small-Is-the-Best 109
C Analysis: Nominal-Is-the-Best 113
5.6 Comments on the Taguchi Method 119
5.7 Problems 119
References 120
6 Statistical Optimization of the Location Parameter 121
6.1 Introduction 121
6.2 Replicated Two-Level Full Factorial Design 123
6.3 Unreplicated Two-Level Full Factorial Design 128
6.4 Two-Level Fractional Factorial Design 133
6.5 Problems 138
References 141
7 Statistical Minimization of the Dispersion Parameter 143
7.1 Introduction 143
7.2 Replicated Study 143
A Analysis of Variance Techniques 143
B Normal Probability Plot of Effects 149
7.3 Unreplicated Study 150
7.4 Problems 154
References 154
8 Validity of the Prediction Equation 155
8.1 Introduction 155
8.2 Graphic Analysis 155
8.3 Adjusted Coefficient of Determination 163
8.4 F Test for Lack of Fit 164
8.5 Analysis Recommendation 167
8.6 Problems 169
References 169
9 Three-Level Factorial Designs 171
9.1 Introduction 171
9.2 Three-Level Full Factorial Design 171
9.3 Box-Behnken Designs 174
9.4 Central Composite Designs 177
A Rotatable Central Composite Design 178
B Face Centered Central Composite Design 187
9.5 Three-Level Taguchi Designs 188
9.6 Problems 190
References 191
10 Second-Order Analysis 193
10.1 Introduction 193
10.2 Second-Order Model in Matrix Terms 193
10.3 Estimation of the Second-Order Model Parameters 195
10.4 Estimation of the First-Order Model Parameters 196
10.5 Fitting a Second-Order Model 198
10.6 Inferences about Regression Parameters 201
10.7 Confidence Limits for Predicted Values 202
10.8 Validity of the Prediction Equation 205
10.9 Quadratic Optimization 205
A Stationary Point 206
B Optimal Point 206
10.10 Problems 212
References 213
Appendices
Appendix 1 Two-Level Fractional Factorial Designs 215
Appendix 2 Plackett-Burman Designs 219
Appendix 3 Taguchi Designs 221
Appendix 4 Standardized Normal Distribution 225
Appendix 5 Percentiles of the t Distribution 227
Appendix 6 Percentiles of the F Distribution 229
Appendix 7 Some Useful Box-Behnken Designs 239
Appendix 8 Matrix Algebra 241
8.1 Matrices 241
8.2 Matrix Addition and Subtraction 243
8.3 Matrix Multiplication 243
8.4 Special Types of Matrices 244
8.5 Inverse of a Matrix 245
Index 249
