Some results on \(s^{n-k}\) fractional factorial designs with minimum aberration or optimal moments. (English) Zbl 0725.62068

Summary: The minimum aberration criterion is commonly used for selecting good fractional factorial designs. In this paper we obtain minimum aberration \(2^{n-k}\) designs for \(k=3,4\) and any n. For \(k>4\) analogous results are not available for general n since the resolution criterion is not periodic for general n and \(k>4\). However, it can be shown that for any fixed k, both the resolution criterion and the minimum aberration criterion have a periodicity property in n for \(s^{n-k}\) designs with large n. Furthermore, the optimal-moments criterion is periodic for any n and k.


62K15 Factorial statistical designs
62K05 Optimal statistical designs
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