Open Access
April 2012 Uniform fractional factorial designs
Yu Tang, Hongquan Xu, Dennis K. J. Lin
Ann. Statist. 40(2): 891-907 (April 2012). DOI: 10.1214/12-AOS987


The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical structures and statistical properties. In this paper uniformity is used to further distinguish fractional factorial designs, besides the minimum aberration criterion. We show that minimum aberration designs have low discrepancies on average. An efficient method for constructing uniform minimum aberration designs is proposed and optimal designs with 27 and 81 runs are obtained for practical use. These designs have good uniformity and are effective for studying quantitative factors.


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Yu Tang. Hongquan Xu. Dennis K. J. Lin. "Uniform fractional factorial designs." Ann. Statist. 40 (2) 891 - 907, April 2012.


Published: April 2012
First available in Project Euclid: 1 June 2012

zbMATH: 1274.62505
MathSciNet: MR2985937
Digital Object Identifier: 10.1214/12-AOS987

Primary: 62K15

Keywords: Discrepancy , generalized minimum aberration , generalized word-length pattern , geometrical isomorphism , uniform minimum aberration design

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 2 • April 2012
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