Regular Article
On the Isomorphism of Fractional Factorial Designs

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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.

Keywords

factorial designs
Hamming distance
isomorphism
uniformity

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This work was partially supported by a Hong Kong RGC grant and Science Faculty of Hong Kong Baptist University. Dennis Lin is partially supported by the National Science Foundation via Grant DMS-9704711 and the National Science Council of ROC via Contract NSC 87-2119-M-001-007. The corresponding author is Kai-Tai Fang.