Mukerjee / Wu A Modern Theory of Factorial Design

1. Auflage 2007
ISBN: 978-0-387-37344-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 226 Seiten

Reihe: Springer Series in Statistics

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.

Autoren/Hrsg.

Mukerjee, Rahul

Wu, C. F. J.

Inhaltsverzeichnis

1;Preface;9
2;Contents;11
3;1 Introduction and Overview;13
3.1;1.1 Prologue;13
3.2;1.2 Why This Book?;15
3.3;1.3 What Is in the Book?;16
3.4;1.4 Beyond the Book;18
4;2 Fundamentals of Factorial Designs;21
4.1;2.1 Factorial Effects;21
4.2;2.2 Kronecker Product Formulation for Factorial Effects;24
4.3;2.3 A Representation for Factorial Effects in Symmetrical Factorials;30
4.4;2.4 Regular Fractions;36
4.5;2.5 Optimality Criteria: Resolution and Minimum Aberration;44
4.6;2.6 Connection with Orthogonal Arrays;47
4.7;2.7 Connection with Finite Projective Geometry;51
4.8;2.8 Algebraic Coding Theory;57
4.9;Exercises;59
5;3 Two-Level Fractional Factorial Designs;61
5.1;3.1 Basic Definitions Revisited;61
5.2;3.2 Minimum Aberration 2n-k Designs with k = 4;64
5.3;3.3 Minimum Aberration Designs via Complementary Designs;69
5.4;3.4 Clear Effects and the MaxC2 Criterion;75
5.5;3.5 Description and Use of the Two-Level Design Tables;79
5.6;Exercises;80
5.7;Appendix 3A.;82
6;4 Fractional Factorial Designs: General Case;97
6.1;4.1 Three-Level Designs;97
6.2;4.2 Minimum Aberration sn k Designs with Small k;99
6.3;4.3 A General Result on Complementary Designs;103
6.4;4.4 Minimum Aberration sn k Designs via Complementary Designs;110
6.5;4.5 Description and Use of the Three-Level Design Tables;114
6.6;Exercises;115
6.7;Appendix 4A. ;116
7;5 Designs with Maximum Estimation Capacity;121
7.1;5.1 Preliminaries;121
7.2;5.2 Connection with Complementary Sets;125
7.3;5.3 Estimation Capacity in 2n Factorials;128
7.4;5.4 Estimation Capacity in sn Factorials;133
7.5;Exercises;135
8;6 Minimum Aberration Designs for Mixed Factorials;136
8.1;6.1 Construction of 4p × 2n Designs via the Method of Replacement;136
8.2;6.2 Minimum Aberration 4p × 2n Designs with p = 1, 2;138
8.3;6.3 Designs for (sr) × sn Factorials: Preliminaries;144
8.4;6.4 Minimum Aberration Designs for (sr) × sn Factorials;150
8.5;6.5 Designs for (sr1) × ( sr2) × sn Factorials;154
8.6;Exercises;160
9;7 Block Designs for Symmetrical Factorials;162
9.1;7.1 Optimal Block Designs for Full Factorials;162
9.2;7.2 Block Designs for Fractional Factorials;165
9.3;7.3 A Projective Geometric Formulation;169
9.4;7.4 Design Criteria;172
9.5;7.5 Description and Use of Block Design Tables;177
9.6;Exercises;178
9.7;Appendix 7A ;180
10;8 Fractional Factorial Split-Plot Designs;192
10.1;8.1 Description and Salient Features;192
10.2;8.2 Design Criteria;195
10.3;8.3 A Projective Geometric Formulation;197
10.4;8.4 Use of Complementary Sets;200
10.5;8.5 Tables of Optimal Designs;202
10.6;Exercises;206
11;9 Robust Parameter Design;207
11.1;9.1 Control and Noise Factors;207
11.2;9.2 Cross Arrays;208
11.3;9.3 Modeling Strategies;211
11.4;9.4 Single Arrays;212
11.5;9.5 Effect Ordering Principle;216
11.6;9.6 Design Criteria;217
11.7;Exercises;219
12;References;221
13;Author Index;227
14;Subject Index;229