Connections Among Different Criteria for Asymmetrical Fractional Factorial Designs

In recent years, there has been increasing interest in the study of asymmetrical fractional factorial designs. Various new optimality criteria have been proposed from different principles for design construction and comparison, such as generalized minimum aberration, minimum moment aberration, minimum projection uniformity and the χ2(D) (for design D) criteria. In this paper, these criteria are reviewed and the χ2(D) criterion is generalized to the so-called minimum χ2 criterion. Connections among different criteria are investigated. These connections provide strong statistical justification for each of them. Some general optimality results are developed, which not only unify several results (including results for the symmetrical case), but also are useful for constructing asymmetrical supersaturated designs.