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On the isomorphism of fractional factorial designs. (English) Zbl 0979.62055
Summary: 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.
We propose a new algorithm based on the centered $$L_2$$-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.

##### MSC:
 62K15 Factorial statistical designs 68Q25 Analysis of algorithms and problem complexity
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