A Modern Theory of Factorial Design

by Mukerjee, Rahul; Wu, C. F. Jeff

• ISBN13: 9780387319919
• ISBN10: 0387319913
• Format: Hardcover
• Copyright: 2006-06-30
• Publisher: Springer Verlag

Summary

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.

Author Biography

C. F. Jeff Wu is a Coca Cola Chair Professor in Engineering Statistics at Georgia Institute of Technology. Rahul Mukerjee is a Professor of Statistics at the Indian Institute of Management Calcutta.

Table of Contents

1 Introduction and Overview	1	(8)
1.1 Prologue	1	(2)
1.2 Why This Book?	3	(1)
1.3 What Is in the Book?	4	(2)
1.4 Beyond the Book	6	(3)
2 Fundamentals of Factorial Designs	9	(40)
2.1 Factorial Effects	9	(3)
2.2 Kronecker Product Formulation for Factorial Effects	12	(6)
2.3 A Representation for Factorial Effects in Symmetrical Factorials	18	(6)
2.4 Regular Fractions	24	(8)
2.5 Optimality Criteria: Resolution and Minimum Aberration	32	(3)
2.6 Connection with Orthogonal Arrays	35	(4)
2.7 Connection with Finite Projective Geometry	39	(6)
2.8 Algebraic Coding Theory	45	(4)
3 Two-Level Fractional Factorial Designs	49	(36)
3.1 Basic Definitions Revisited	49	(8)
3.2 Minimum Aberration 2n-k Designs with k less than or equal to 4 52
3.3 Minimum Aberration Designs via Complementary Designs	57	(6)
3.4 Clear Effects and the MaxC2 Criterion	63	(4)
3.5 Description and Use of the Two-Level Design Tables	67	(18)
4 Fractional Factorial Designs: General Case	85	(24)
4.1 Three-Level Designs	85	(2)
4.2 Minimum Aberration Sn-k Designs with Small k	87	(4)
4.3 A General Result on Complementary Designs	91	(7)
4.4 Minimum Aberration Sn-k Designs via Complementary Designs	98	(4)
4.5 Description and Use of the Three-Level Design Tables	102	(7)
5 Designs with Maximum Estimation Capacity	109	(16)
5.1 Preliminaries	109	(4)
5.2 Connection with Complementary Sets	113	(3)
5.3 Estimation Capacity in 2n Factorials	116	(5)
5.4 Estimation Capacity in sn Factorials	121	(4)
6 Minimum Aberration Designs for Mixed Factorials	125	(26)
6.1 Construction of 4p x 2n Designs via the Method of Replacement	125	(2)
6.2 Minimum Aberration 4p x 2n Designs with p = 1, 2	127	(6)
6.3 Designs for (sr) x sn Factorials: Preliminaries	133	(6)
6.4 Minimum Aberration Designs for (sr) x sn Factorials	139	(4)
6.5 Designs for (sr1) x (sr2) x sn Factorials	143	(8)
7 Block Designs for Symmetrical Factorials	151	(30)
7.1 Optimal Block Designs for Full Factorials	151	(3)
7.2 Block Designs for Fractional Factorials	154	(4)
7.3 A Projective Geometric Formulation	158	(3)
7.4 Design Criteria	161	(5)
7.5 Description and Use of Block Design Tables	166	(15)
8 Fractional Factorial Split-Plot Designs	181	(16)
8.1 Description and Salient Features	181	(3)
8.2 Design Criteria	184	(2)
8.3 A Projective Geometric Formulation	186	(3)
8.4 Use of Complementary Sets	189	(2)
8.5 Tables of Optimal Designs	191	(6)
9 Robust Parameter Design	197	(14)
9.1 Control and Noise Factors	197	(1)
9.2 Cross Arrays	198	(3)
9.3 Modeling Strategies	201	(1)
9.4 Single Arrays	202	(4)
9.5 Effect Ordering Principle	206	(1)
9.6 Design Criteria	207	(4)
References	211	(6)
Author Index	217	(2)
Subject Index	219