Abstract: A novel combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs. The new criterion, which is to sequentially minimize the power moments of the number of coincidences among runs, is a surrogate with tremendous computational advantages for many statistically justified criteria, such as minimum-aberration, generalized minimum aberration and
. In addition, the minimum moment aberration is conceptually simple and convenient for theoretical development. The general theory developed here not only unifies several results, but also provides novel results on nonregular and supersaturated designs.
Key words and phrases: Complementary design, fractional factorial design, generalized minimum aberration, orthogonal array, Pless power moment identity.