Statistica Sinica 13(2003), 403-408

SOME PROPERTIES OF BLOCKED AND UNBLOCKED

FOLDOVERS OF $2^{k-p}$ DESIGNS

Kenny Q. Ye and William Li

State University of New York at Stony Brook and University of Minnesota

Abstract: In this article, we focus on the theoretical properties of the foldover design and the resulting combined design obtained by augmenting an initial design by its foldover. We prove that there are $2^p$ distinct ways to fold over a $2^{k-p}$ design. Optimal foldover plans are also discussed. We investigate the impact of the inclusion of a blocking variable to the design. We show that the minimum aberration foldover design with the presence of the blocking effect is the same as the one without blocking.

Key words and phrases: Minimum aberration, optimal foldover, resolution, word length pattern.