On the isomorphism of fractional factorial designs

Chang-Xing Ma*, Kai-Tai Fang, Dennis K. J. Lin

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

41 Citations (Scopus)

Abstract

Two fractional factorial designs are called isomorphic if one can be obtained from the other by relabeling the factors, reordering the runs, and switching the levels of factors. To identify the isomorphism of two s-factor n-run designs is known to be an NP hard problem, when n and s increase. There is no tractable algorithm for the identification of isomorphic designs. In this paper, we propose a new algorithm based on the centered L2-discrepancy, a measure of uniformity, for detecting the isomorphism of fractional factorial designs. It is shown that the new algorithm is highly reliable and can significantly reduce the complexity of the computation. Theoretical justification for such an algorithm is also provided. The efficiency of the new algorithm is demonstrated by using several examples that have previously been discussed by many others.

Original languageEnglish
Pages (from-to)86-97
Number of pages12
JournalJournal of Complexity
Volume17
Issue number1
DOIs
Publication statusPublished - Mar 2001
Externally publishedYes

Scopus Subject Areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • General Mathematics
  • Control and Optimization
  • Applied Mathematics

User-Defined Keywords

  • Factorial designs
  • Hamming distance
  • Isomorphism
  • Uniformity

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