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.