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April 2001 Blocked regular fractional factorial designs with maximum estimation capacity
Ching-Shui Cheng, Rahul Mukerjee
Ann. Statist. 29(2): 530-548 (April 2001). DOI: 10.1214/aos/1009210551

Abstract

In this paper, the problem of constructing optimal blocked regular fractional factorial designs is considered. The concept of minimum aberration due to Fries and Hunter is a well­accepted criterion for selecting good unblocked fractional factorial designs. Cheng, Steinberg and Sun showed that a minimum aberration design of resolution three or higher maximizes the number of two­factor interactions which are not aliases of main effects and also tends to distribute these interactions over the alias sets very uniformly. We extend this to construct block designs in which (i) no main effect is aliased with any other main effect not confounded with blocks, (ii) the number of two­factor interactions that are neither aliased with main effects nor confounded with blocks is as large as possible and (iii) these interactions are distributed over the alias sets as uniformly as possible. Such designs perform well under the criterion of maximum estimation capacity, a criterion of model robustness which has a direct statistical meaning. Some general results on the construction of blocked regular fractional factorial designs with maximum estimation capacity are obtained by using a finite projective geometric approach.

Citation

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Ching-Shui Cheng. Rahul Mukerjee. "Blocked regular fractional factorial designs with maximum estimation capacity." Ann. Statist. 29 (2) 530 - 548, April 2001. https://doi.org/10.1214/aos/1009210551

Information

Published: April 2001
First available in Project Euclid: 24 December 2001

zbMATH: 1041.62064
MathSciNet: MR1863968
Digital Object Identifier: 10.1214/aos/1009210551

Subjects:
Primary: 62K15

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 2 • April 2001
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