Minimum $G_2$-aberration for nonregular fractional factorial designs

Deng and Tang proposed generalized resolution and minimum aberra- tion criteria for comparing and assessing nonregular fractional factorials, of which Plackett–Burman designs are special cases. A relaxed variant of generalized aberration is proposed and studied in this paper. We show that a best design according to this criterion minimizes the contamination of nonnegligible interactions on the estimation of main effects in the order of importance given by the hierarchical assumption. The new criterion is defined through a set of B values, a generalization of word length pattern. We derive some theoretical results that relate the B values of a nonregu- lar fractional factorial and those of its complementary design. Application of this theory to the construction of the best designs according to the new aberration criterion is discussed. The results in this paper generalize those in Tang and Wu, which characterize a minimum aberration (regular) 2 m − k design through its complementary design.