Fractional Factorial Plans

by Dey, Aloke; Mukerjee, Rahul

• ISBN13: 9780471294146
• ISBN10: 0471294144
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-03-25
• Publisher: Wiley-Interscience

Summary

A one-stop reference to fractional factorials and related orthogonal arrays. Presenting one of the most dynamic areas of statistical research, this book offers a systematic, rigorous, and up-to-date treatment of fractional factorial designs and related combinatorial mathematics. Leading statisticians Aloke Dey and Rahul Mukerjee consolidate vast amounts of material from the professional literature--expertly weaving fractional replication, orthogonal arrays, and optimality aspects. They develop the basic theory of fractional factorials using the calculus of factorial arrangements, thereby providing a unified approach to the study of fractional factorial plans. An indispensable guide for statisticians in research and industry as well as for graduate students, Fractional Factorial Plans features: * Construction procedures of symmetric and asymmetric orthogonal arrays. * Many up-to-date research results on nonexistence. * A chapter on optimal fractional factorials not based on orthogonal arrays. * Trend-free plans, minimum aberration plans, and search and supersaturated designs. * Numerous examples and extensive references.

Author Biography

ALOKE DEY, PhD, is a professor at the Indian Statistical Institute in New Delhi. An elected member of the International Statistical Institute, Dr. Dey is widely published in the field, including many research papers and two books. RAHUL MUKERJEE, PhD, is a professor at the Indian Institute of Management in Calcutta. A member of the editorial board for several statistics journals, Dr. Mukerjee has authored and coauthored many research papers and two books. Dr. Mukerjee is an elected member of the International Statistical Institute.

Table of Contents

Preface	xi
Introduction	1	(6)
Introductory Remarks	1	(1)
Preliminary Ideas	2	(3)
Scope of the Book	5	(2)
Fractional Plans and Orthogonal Arrays	7	(25)
Introduction	7	(1)
Kronecker Notation	7	(4)
Fractional Factorial Plans	11	(7)
Concept of Resolution	18	(2)
Optimality Criteria	20	(3)
Role of Orthogonal Arrays	23	(9)
Exercises	30	(2)
Symmetric Orthogonal Arrays	32	(16)
Introduction	32	(1)
Orthogonal Arrays and Hadamard Matrices	32	(2)
Foldover Technique	34	(2)
Use of Galois Fields	36	(4)
Method of Differences	40	(6)
Some Further Results	46	(2)
Exercises	47	(1)
Asymmetric Orthogonal Arrays	48	(27)
Introduction	48	(1)
Collapsing and Replacement Procedures	48	(2)
Use of Hadamard Matrices	50	(6)
Use of Difference Matrices	56	(4)
Use of Resolvable Arrays	60	(6)
More on the Method of Grouping	66	(2)
Arrays of Higher Strength	68	(7)
Exercises	74	(1)
Some Results on Nonexistence	75	(19)
Introduction	75	(1)
Bose-Bush Approach	75	(4)
Linear Programming and Other Bounds	79	(5)
On the Tight and Nearly Tight Cases	84	(10)
Exercises	93	(1)
More on Optimal Fractional Plans and Related Topics	94	(46)
Introduction and Preliminaries	94	(1)
Augmented Orthogonal Arrays: Addition of One Run	95	(7)
Augmented Orthogonal Arrays: Further Results	102	(15)
Nearly Orthogonal Arrays	117	(5)
Connection with Weighing Designs	122	(6)
Optimality with Two or Three Factors	128	(6)
Some Other Plans	134	(6)
Exercises	139	(1)
Trend-Free Plans and Blocking	140	(22)
Introduction	140	(1)
Trend-Free Plans: Basic Principles	140	(7)
Trend-Free Orthogonal Arrays	147	(11)
Blocking	158	(4)
Exercises	161	(1)
Some Further Developments	162	(25)
Introduction	162	(1)
Regular Fractions and Minimum Aberration Designs	162	(13)
Search Designs	175	(7)
Supersaturated Designs	182	(5)
Exercises	184	(3)
Appendix	187	(1)
A.1 Hadamard Matrices	187	(2)
A.2 Difference Matrices	189	(1)
A.3 Selected Orthogonal Arrays	190	(5)
References	195	(14)
Index	209