By studying treatment contrasts and ANOVA models, we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs. The criterion is independent of the choice of treatment contrasts and thus model-free. It works for symmetrical and asymmetrical designs, regular and nonregular designs. In particular,it reduces to the minimum aberration criterion for regular designs and the minimum $G_2$-aberration criterion for two-level nonregular designs. In addition, by exploring the connection between factorial design theory and coding theory, we develop a complementary design theory for general symmetrical designs,which covers many existing results as special cases.
"Generalized minimum aberration for asymmetrical fractional factorial designs." Ann. Statist. 29 (4) 1066 - 1077, August 2001. https://doi.org/10.1214/aos/1013699993