Minimum Aberration Designs for Mixed Factorials

Abstract

Extension of the ideas in Chapters 3 and 4 to designs with factors at different numbers of levels is the focus of this chapter. The important special case of mixed two- and four-level designs is first discussed. An extension of the minimum aberration criterion is considered. More generally, designs with one factor at s^r levels and n factors at s levels, or one factor at $s^{r_1 }$ levels, a second factor at $s^{r_2 }$ levels, and n factors at s levels, where s is a prime or prime power, are considered. These designs can be conveniently described and their properties obtained using finite projective geometry. The method of complementary sets is again seen to provide a general approach for finding minimum aberration designs in such settings.