Statistica Sinica 15(2005), 751-765

ASYMMETRIC FRACTIONAL FACTORIAL PLANS

OPTIMAL FOR MAIN EFFECTS AND SPECIFIED

TWO-FACTOR INTERACTIONS

Aloke Dey$^1$, Chung-yi Suen$^2$ and Ashish Das$^1$

$^1$Indian Statistical Institute, New Delhi and $^2$Cleveland State University

Abstract: Fractional factorial plans for asymmetric factorial experiments are obtained. These are shown to be universally optimal within the class of all plans involving the same number of runs under a model that includes the mean, all main effects and a specified set of two-factor interactions. Finite projective geometry is used to obtain such plans for experiments wherein the number of levels of each of the factors and the number of runs is a power of $m$, a prime or a prime power. Methods of construction of optimal plans under the same model are also discussed for the case where the number of levels as well as the number of runs are not necessarily powers of a prime number.

Key words and phrases: Finite projective geometry, Galois field, saturated plans, universal optimality.