Theory of Nonregular Factorial Designs

Ching-Shui Cheng, Boxin Tang

• Publisher: CRC Press
• Year: 2025
• eBook ISBN: 9781040342510
• Edition: 0
• Topic: Mathematics
• Index: Mathematics

Nonregular factorial designs are a class of factorial designs that enable researchers to study simultaneously the effects of many explanatory variables on a response variable of interest. Factorial designs have been in the mainstream of design research for decades, but interest in nonregular factorial designs has been increasing significantly in the last twenty years or so. These designs are practically useful as they offer much richer and more flexible choices for experimenters to contemplate than regular designs. Theoretically, they present new challenges and raise new issues that require new ideas and methods to properly address. This book is the first to synthesize research on this topic into a consistent statistical design framework. It is focused on the theoretical underpinnings of nonregular factorial designs but emphasizes the ideas and methods of statistical designs, rather than mathematical rigor. Some background is provided in an appendix, and the book also includes lots of worked examples to illustrate the ideas and methods.

Features:

• A unified and comprehensive overview of the theory and application of nonregular factorial designs
• Self-contained, with an appendix of necessary background knowledge in factorial designs
• Mathematics is kept to a minimum, with proofs only included if simple or insightful, or is otherwise in chapter appendices
• Great attention has been paid to the narrative flow
• Lots of worked examples to illustrate the ideas and methods

This book is primarily aimed at researchers and practitioners working on the design of experiments. It will be a perfect entry into the field for a junior researcher and a useful reference for all researchers already in the field. It could be used as a textbook for graduate students who have taken a first design course and have a passion for design ideas and research. Scientists from other disciplines will find the book useful as well, if their research involves multi-factor experiments.

Table of contents

• Cover Page
• Half-Title Page
• Series Page
• Title Page
• Copyright Page
• Contents
• Preface
• Author
• 1 Introduction
• 2 Basics of Factorial Designs
• 3 J-Characteristics and Projection Properties
• 4 Generalized Resolution and Minimum G-Aberration
• 5 Minimum G2-Aberration
• 6 Clear Effects, Requirement Sets, and SOS Designs
• 7 Minimum G2-Aberration in Complex Settings
• 8 Supersaturated Designs
• 9 Other Nonregular Designs
• 10 Multi-Level Nonregular Designs
• 11 Mixed-Level Designs and Complicated Unit Structures
• 12 Space-Filling Designs
• A Appendix: Background Knowledge
• References
• Index