A Modern Theory of Factorial Design (eBook)
X, 226 Seiten
Springer New York (Verlag)
978-0-387-37344-7 (ISBN)
The last twenty years have witnessed a significant growth of interest in optimal factorial designs, under possible model uncertainty, via the minimum aberration and related criteria. This book gives, for the first time in book form, a comprehensive and up-to-date account of this modern theory. Many major classes of designs are covered in the book. While maintaining a high level of mathematical rigor, it also provides extensive design tables for research and practical purposes. Apart from being useful to researchers and practitioners, the book can form the core of a graduate level course in experimental design.
Factorial design plays a fundamental role in efficient and economic experimentation with multiple input variables and is extremely popular in various fields of application, including engineering, agriculture, medicine and life sciences. Factorial experiments are often used in case studies in quality management and Design for Six Sigma (DFSS). The last twenty years have witnessed a significant growth of interest in optimal factorial designs, under possible model uncertainty, via the minimum aberration and related criteria. The present book gives, for the first time in book form, a comprehensive and up-to-date account of this modern theory. Many major classes of designs are covered in the book. While maintaining a high level of mathematical rigor, it also provides extensive design tables for research and practical purposes. In order to equip the readers with the necessary background, some foundational concepts and results are developed in Chapter 2. Apart from being useful to researchers and practitioners, the book can form the core of a graduate level course in experimental design. It can also be used for courses in combinatorial designs or combinatorial mathematics.
Preface 9
Contents 11
1 Introduction and Overview 13
1.1 Prologue 13
1.2 Why This Book? 15
1.3 What Is in the Book? 16
1.4 Beyond the Book 18
2 Fundamentals of Factorial Designs 21
2.1 Factorial Effects 21
2.2 Kronecker Product Formulation for Factorial Effects 24
2.3 A Representation for Factorial Effects in Symmetrical Factorials 30
2.4 Regular Fractions 36
2.5 Optimality Criteria: Resolution and Minimum Aberration 44
2.6 Connection with Orthogonal Arrays 47
2.7 Connection with Finite Projective Geometry 51
2.8 Algebraic Coding Theory 57
Exercises 59
3 Two-Level Fractional Factorial Designs 61
3.1 Basic Definitions Revisited 61
3.2 Minimum Aberration 2n-k Designs with k = 4 64
3.3 Minimum Aberration Designs via Complementary Designs 69
3.4 Clear Effects and the MaxC2 Criterion 75
3.5 Description and Use of the Two-Level Design Tables 79
Exercises 80
Appendix 3A. 82
4 Fractional Factorial Designs: General Case 97
4.1 Three-Level Designs 97
4.2 Minimum Aberration sn k Designs with Small k 99
4.3 A General Result on Complementary Designs 103
4.4 Minimum Aberration sn k Designs via Complementary Designs 110
4.5 Description and Use of the Three-Level Design Tables 114
Exercises 115
Appendix 4A. 116
5 Designs with Maximum Estimation Capacity 121
5.1 Preliminaries 121
5.2 Connection with Complementary Sets 125
5.3 Estimation Capacity in 2n Factorials 128
5.4 Estimation Capacity in sn Factorials 133
Exercises 135
6 Minimum Aberration Designs for Mixed Factorials 136
6.1 Construction of 4p × 2n Designs via the Method of Replacement 136
6.2 Minimum Aberration 4p × 2n Designs with p = 1, 2 138
6.3 Designs for (sr) × sn Factorials: Preliminaries 144
6.4 Minimum Aberration Designs for (sr) × sn Factorials 150
6.5 Designs for (sr1) × ( sr2) × sn Factorials 154
Exercises 160
7 Block Designs for Symmetrical Factorials 162
7.1 Optimal Block Designs for Full Factorials 162
7.2 Block Designs for Fractional Factorials 165
7.3 A Projective Geometric Formulation 169
7.4 Design Criteria 172
7.5 Description and Use of Block Design Tables 177
Exercises 178
Appendix 7A 180
8 Fractional Factorial Split-Plot Designs 192
8.1 Description and Salient Features 192
8.2 Design Criteria 195
8.3 A Projective Geometric Formulation 197
8.4 Use of Complementary Sets 200
8.5 Tables of Optimal Designs 202
Exercises 206
9 Robust Parameter Design 207
9.1 Control and Noise Factors 207
9.2 Cross Arrays 208
9.3 Modeling Strategies 211
9.4 Single Arrays 212
9.5 Effect Ordering Principle 216
9.6 Design Criteria 217
Exercises 219
References 221
Author Index 227
Subject Index 229
Erscheint lt. Verlag | 15.1.2007 |
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Reihe/Serie | Springer Series in Statistics | Springer Series in Statistics |
Zusatzinfo | X, 226 p. |
Verlagsort | New York |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Statistik |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Technik | |
Schlagworte | Boundary element method • Design • Factor • Form • Management • Mathematica • Mathematics • Maximum • Medicine • Minimum • Model • Quality management • Time • Uncertainty • Variable |
ISBN-10 | 0-387-37344-6 / 0387373446 |
ISBN-13 | 978-0-387-37344-7 / 9780387373447 |
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