Open Access
April 2005 A general theory of minimum aberration and its applications
Ching-Shui Cheng, Boxin Tang
Ann. Statist. 33(2): 944-958 (April 2005). DOI: 10.1214/009053604000001228


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.


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Ching-Shui Cheng. Boxin Tang. "A general theory of minimum aberration and its applications." Ann. Statist. 33 (2) 944 - 958, April 2005.


Published: April 2005
First available in Project Euclid: 26 May 2005

zbMATH: 1068.62086
MathSciNet: MR2163164
Digital Object Identifier: 10.1214/009053604000001228

Primary: 62K15

Keywords: blocking , design resolution , Fractional factorial design , linear graph , orthogonal array , requirement set , robust parameter design , split plot design

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.33 • No. 2 • April 2005
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