On the isomorphism of fractional factorial designs

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

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


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 (US)
Pages (from-to)86-97
Number of pages12
JournalJournal of Complexity
Issue number1
StatePublished - Mar 2001

All Science Journal Classification (ASJC) codes

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


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