Optimal Design of Experiments A Case Study

This book demonstrates the utility of the computer-aided optimal design approach using real industrial examples. These examples address questions such as the following: "#xA0;How can I do screening inexpensively if I have dozens of factors to investigate? "#xA0;What can I do if I have day-to-day variability and I can only perform 3 runs a day? "#xA0;How can I do RSM cost effectively if I have categorical factors? "#xA0;How can I design and analyze experiments when there is a factor that can only be changed a few times over the study? "#xA0;How can I include both ingredients in a mixture and processing factors in the same study? "#xA0;How can I design an experiment if there are many factor combinations that are impossible to run? "#xA0;How can I make sure that a time trend due to warming up of equipment does not affect the conclusions from a study? "#xA0;How can I take into account batch information in when designing experiments involving multiple batches? "#xA0;How can I add runs to a botched experiment to resolve ambiguities? While answering these questions the book also shows how to evaluate and compare designs. This allows researchers to make sensible trade-offs between the cost of experimentation and the amount of information they obtain. The structure of the book is organized around the following chapters: 1)#xA0;Introduction explaining the concept of tailored DOE. 2)#xA0;Basics of optimal design. 3)#xA0;Nine case studies dealing with the above questions using the flow: "#xA0;description #x92; design #x92; analysis #x92; optimization or engineering interpretation. 4)#xA0;Summary. 5)#xA0;Technical appendices for the mathematically curious.

Peter Goos, University of Antwerp and Erasmus University Rotterdam Bradley Jones, JMP Division of SAS

Preface	p. xiii
Acknowledgments	p. xv
A simple comparative experiment	p. 1
Key concepts	p. 1
The setup of a comparative experiment	p. 2
Summary	p. 8
An optimal screening experiment	p. 9
Key concepts	p. 9
Case: an extraction experiment	p. 10
Problem and design	p. 10
Data analysis	p. 14
Peek into the black box	p. 21
Main-effects models	p. 21
Models with two-factor interaction effects	p. 22
Factor scaling	p. 24
Ordinary least squares estimation	p. 24
Significance tests and statistical power calculations	p. 27
Variance inflation	p. 28
Aliasing	p. 29
Optimal design	p. 33
Generating optimal experimental designs	p. 35
The extraction experiment revisited	p. 40
Principles of successful screening: sparsity, hierarchy, and heredity	p. 41
Background reading	p. 44
Screening	p. 44
Algorithms for finding optimal designs	p. 44
Summary	p. 45
Adding runs to a screening experiment	p. 47
Key concepts	p. 47
Case: an augmented extraction experiment	p. 48
Problem and design	p. 48
Data analysis	p. 55
Peek into the black box	p. 59
Optimal selection of a follow-up design	p. 60
Design construction algorithm	p. 65
Foldover designs	p. 66
Background reading	p. 67
Summary	p. 67
A response surface design with a categorical factor	p. 69
Key concepts	p. 69
Case: a robust and optimal process experiment	p. 70
Problem and design	p. 70
Data analysis	p. 79
Peek into the black box	p. 82
Quadratic effects	p. 82
Dummy variables for multilevel categorical factors	p. 83
Computing D-efficiencies	p. 86
Constructing Fraction of Design Space plots	p. 87
Calculating the average relative variance of prediction	p. 88
Computing I-efficiencies	p. 90
Ensuring the validity of inference based on ordinary least squares	p. 90
Design regions	p. 91
Background reading	p. 92
Summary	p. 93
A response surface design in an irregularly shaped design region	p. 95
Key concepts	p. 95
Case: the yield maximization experiment	p. 95
Problem and design	p. 95
Data analysis	p. 103
Peek into the black box	p. 108
Cubic factor effects	p. 108
Lack-of-fit test	p. 109
Incorporating factor constraints in the design construction algorithm	p. 111
Background reading	p. 112
Summary	p. 112
A "mixture" experiment with process variables	p. 113
Key concepts	p. 113
Case: the rolling mill experiment	p. 114
Problem and design	p. 114
Data analysis	p. 121
Peek into the black box	p. 123
The mixture constraint	p. 123
The effect of the mixture constraint on the model	p. 123
Commonly used models for data from mixture experiments	p. 125
Optimal designs for mixture experiments	p. 127
Design construction algorithms for mixture experiments	p. 130
Background reading	p. 132
Summary	p. 133
A response surface design in blocks	p. 135
Key concepts	p. 135
Case: the pastry dough experiment	p. 136
Problem and design	p. 136
Data analysis	p. 144
Peek into the black box	p. 151
Model	p. 151
Generalized least squares estimation	p. 153
Estimation of variance components	p. 156
Significance tests	p. 157
Optimal design of blocked experiments	p. 157
Orthogonal blocking	p. 158
Optimal versus orthogonal blocking	p. 160
Background reading	p. 160
Summary	p. 161
A screening experiment in blocks	p. 163
Key concepts	p. 163
Case: the stability improvement experiment	p. 164
Problem and design	p. 164
Afterthoughts about the design problem	p. 169
Data analysis	p. 175
Peek into the black box	p. 179
Models involving block effects	p. 179
Fixed block effects	p. 182
Background reading	p. 184
Summary	p. 185
Experimental design in the presence of covariates	p. 187
Key concepts	p. 187
Case: the polypropylene experiment	p. 188
Problem and design	p. 188
Data analysis	p. 197
Peek into the black box	p. 206
Covariates or concomitant variables	p. 206
Models and design criteria in the presence of covariates	p. 206
Designs robust to time trends	p. 211
Design construction algorithms	p. 215
To randomize or not to randomize	p. 215
Final thoughts	p. 216
Background reading	p. 216
Summary	p. 217
A split-plot design	p. 219
Key concepts	p. 219
Case: the wind tunnel experiment	p. 220
Problem and design	p. 220
Data analysis	p. 232
Peek into the black box	p. 240
Split-plot terminology	p. 240
Model	p. 242
Inference from a split-plot design	p. 244
Disguises of a split-plot design	p. 247
Required number of whole plots and runs	p. 249
Optimal design of split-plot experiments	p. 250
A design construction algorithm for optimal split-plot designs	p. 251
Difficulties when analyzing data from split-plot experiments	p. 253
Background reading	p. 253
Summary	p. 254
A two-way split-plot design	p. 255
Key concepts	p. 255
Case: the battery cell experiment	p. 255
Problem and design	p. 255
Data analysis	p. 263
Peek into the black box	p. 267
The two-way split-plot model	p. 269
Generalized least squares estimation	p. 270
Optimal design of two-way split-plot experiments	p. 273
A design construction algorithm for D-optimal two-way split-plot designs	p. 273
Extensions and related designs	p. 274
Background reading	p. 275
Summary	p. 276
Bibliography	p. 277
Index	p. 283
Table of Contents provided by Ingram. All Rights Reserved.

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Optimal Design of Experiments A Case Study Approach

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