## The Annals of Statistics

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

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

Shao-Wei Cheng and Kenny Q. Ye

#### 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

**Keywords**

Indicator function polynomial models generalized wordlength pattern.

#### 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