The Annals of Statistics

Uniform fractional factorial designs

Yu Tang, Hongquan Xu, and Dennis K. J. Lin

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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.

Article information

Ann. Statist. Volume 40, Number 2 (2012), 891-907.

First available in Project Euclid: 1 June 2012

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Zentralblatt MATH identifier

Primary: 62K15: Factorial designs

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


Tang, Yu; Xu, Hongquan; Lin, Dennis K. J. Uniform fractional factorial designs. Ann. Statist. 40 (2012), no. 2, 891--907. doi:10.1214/12-AOS987.

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