## The Annals of Statistics

### A general theory of minimum aberration and its applications

#### Abstract

Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question its importance and usefulness nowadays. In the past decade or so, a great deal of work has been done on minimum aberration and its various extensions. This paper develops a general theory of minimum aberration based on a sound statistical principle. Our theory provides a unified framework for minimum aberration and further extends the existing work in the area. More importantly, the theory offers a systematic method that enables experimenters to derive their own aberration criteria. Our general theory also brings together two seemingly separate research areas: one on minimum aberration designs and the other on designs with requirement sets. To facilitate the design construction, we develop a complementary design theory for quite a general class of aberration criteria. As an immediate application, we present some construction results on a weak version of this class of criteria.

#### Article information

Source
Ann. Statist., Volume 33, Number 2 (2005), 944-958.

Dates
First available in Project Euclid: 26 May 2005

https://projecteuclid.org/euclid.aos/1117114341

Digital Object Identifier
doi:10.1214/009053604000001228

Mathematical Reviews number (MathSciNet)
MR2163164

Zentralblatt MATH identifier
1068.62086

Subjects
Primary: 62K15: Factorial designs

#### Citation

Cheng, Ching-Shui; Tang, Boxin. A general theory of minimum aberration and its applications. Ann. Statist. 33 (2005), no. 2, 944--958. doi:10.1214/009053604000001228. https://projecteuclid.org/euclid.aos/1117114341

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