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October 2004 Geometric isomorphism and minimum aberration for factorial designs with quantitative factors
Shao-Wei Cheng, Kenny Q. Ye
Ann. Statist. 32(5): 2168-2185 (October 2004). DOI: 10.1214/009053604000000599

Abstract

Factorial designs have broad applications in agricultural, engineering and scientific studies. In constructing and studying properties of factorial designs, traditional design theory treats all factors as nominal. However, this is not appropriate for experiments that involve quantitative factors. For designs with quantitative factors, level permutation of one or more factors in a design matrix could result in different geometric structures, and, thus, different design properties. In this paper indicator functions are introduced to represent factorial designs. A polynomial form of indicator functions is used to characterize the geometric structure of those designs. Geometric isomorphism is defined for classifying designs with quantitative factors. Based on indicator functions, a new aberration criteria is proposed and some minimum aberration designs are presented.

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Shao-Wei Cheng. Kenny Q. Ye. "Geometric isomorphism and minimum aberration for factorial designs with quantitative factors." Ann. Statist. 32 (5) 2168 - 2185, October 2004. https://doi.org/10.1214/009053604000000599

Information

Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1056.62088
MathSciNet: MR2102507
Digital Object Identifier: 10.1214/009053604000000599

Subjects:
Primary: 62K15 , 62K20

Keywords: generalized wordlength pattern. , Indicator function , polynomial models

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 5 • October 2004
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