Abstract
Various optimal criteria have been proposed to rank asymmetrical frac- tional factorial designs. Among them, the generalized minimum aberration and the minimum moment aberration criteria are the most popular ones and have received much attention. Recently, Liu et al. (Stat Sin 16:1285-1297, 2006) proposed the mini- mum χ 2 criterion in terms of level-combinations. In this paper, the equivalency of the generalized minimum aberration and the minimum χ 2 criteria is reported, which not only provides another justification for each other but also develops some theoretical results for designs with generalized minimum aberration and some lower bounds for the generalized wordlength pattern. Besides, an analytic relationship between gener- alized minimum aberration and minimum moment aberration is obtained for asym- metrical fractional factorial designs.
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