Statistica Sinica 11(2001), 225-239

MINIMUM ABERRATION DESIGNS FOR MIXED FACTORIALS

IN TERMS OF COMPLEMENTARY SETS

Rahul Mukerjee and C. F. J. Wu

Indian Institute of Management and University of Michigan

Abstract: Minimum aberration designs are obtained for two types of mixed-level fractional factorial: (i) $(s^r) \times s^n$ factorial, and (ii) $(s^{r_{1}}) \times (s^{r_{2}}) \times s^n$ factorial, where $s$ is any prime or prime power, and $r , r_1, r_2$ and $n$ are positive integers. Projective geometric tools are employed to find the wordlength pattern of a given design in terms of that of its complementary set. Many useful designs are found and tabulated.

Key words and phrases: Fractional factorial designs, main effect fractions, projective geometry.