Statistica Sinica 11(2001), 213-223

MINIMUM ABERRATION $(S^2)S^{n-k}$ DESIGNS

Runchu Zhang and Qin Shao

Nankai University and University of Georgia

Abstract: This paper extends the $4^m 2^n$ minimum aberration designs (MA designs) of Wu and Zhang (1993) to the case of $(S^2)S^{n-k}$, where $S$ is any prime or prime power. Some basic properties of $(S^2)S^{n-k}$ MA designs, including the relations with $S^{n-k}$ MA designs, are discussed. The $(9)3^{n-k}$ MA designs with 27 runs and $(16)4^{n-k}$ MA designs with 64 runs are tabulated, and some $(4)2^{n-k}$ MA designs are constructed using the above relations.

Key words and phrases: Asymmetrical factorial design, fractional factorial designs, grouping scheme, minimum aberration.