The Annals of Statistics
- Ann. Statist.
- Volume 40, Number 2 (2012), 891-907.
Uniform fractional factorial designs
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.
Ann. Statist. Volume 40, Number 2 (2012), 891-907.
First available in Project Euclid: 1 June 2012
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Primary: 62K15: Factorial designs
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. http://projecteuclid.org/euclid.aos/1338515141.