Geometric isomorphism and minimum aberration for factorial designs with quantitative factors

Shao Wei Cheng, Kenny Q. Ye

Research output: Contribution to journalArticlepeer-review

98 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2168-2185
Number of pages18
JournalAnnals of Statistics
Issue number5
StatePublished - Oct 2004


  • Generalized wordlength pattern
  • Indicator function
  • Polynomial models

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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