Geometric isomorphism and minimum aberration for factorial designs with quantitative factors

Details Geometric isomorphism and minimum aberration for factorial designs with quantitative factors Geometric isomorphism and minimum aberration for factorial designs with quantitative factors

2005-03-29

arxiv.org/abs/math/0503678v1

Annals of Statistics 2004, Vol. 32, No. 5, 2168-2185

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000599 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000599

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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