Projection justification of generalized minimum aberration for asymmetrical fractional factorial designs

Abstract.

Recently, Xu and Wu (2001) presented generalized minimum aberration criterion for comparing and selecting general fractional factorial designs. This criterion is defined using a set of χ _u (D) values, called J-characteristics by us. In this paper, we find a set of linear equations that relate the set of design points to that of J-characteristics, which implies that a factorial design is uniquely determined by its J-characteristics once the orthonormal contrasts are designated. Thereto, a projection justification of generalized minimum aberration is established. All of these conclusions generalize the results for two-level symmetrical factorial designs in Tang (2001).