Generalized Minimum Aberration for Asymmetrical Fractional Factorial Designs

• Activity Number: 180
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical & Engineering Sciences*
• Author(s): Hongquan Xu*+ and Jeff Wu
• Affiliation(s): University of California, Los Angeles and University of Michigan
• Keywords: distance distribution ; orthogonal arrays ; minimum aberration ; MacWilliams transforms ; wordlength pattern

Abstract

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.