## The Annals of Statistics

### Uniform fractional factorial designs

#### Abstract

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

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

Dates
First available in Project Euclid: 1 June 2012

http://projecteuclid.org/euclid.aos/1338515141

Digital Object Identifier
doi:10.1214/12-AOS987

Mathematical Reviews number (MathSciNet)
MR2985937

Zentralblatt MATH identifier
1274.62505

Subjects
Primary: 62K15: Factorial designs

#### Citation

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.

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