## The Annals of Statistics

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

#### 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.

#### Article information

Source
Ann. Statist., Volume 32, Number 5 (2004), 2168-2185.

Dates
First available in Project Euclid: 27 October 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1098883786

Digital Object Identifier
doi:10.1214/009053604000000599

Mathematical Reviews number (MathSciNet)
MR2102507

Zentralblatt MATH identifier
1056.62088

Subjects
Primary: 62K15: Factorial designs 62K20: Response surface designs

#### Citation

Cheng, Shao-Wei; Ye, Kenny Q. Geometric isomorphism and minimum aberration for factorial designs with quantitative factors. Ann. Statist. 32 (2004), no. 5, 2168--2185. doi:10.1214/009053604000000599. https://projecteuclid.org/euclid.aos/1098883786

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