Regular fractional factorial designs with minimum aberration and maximum estimation capacity

Abstract

Using the approach of finite projective geometry, we make a systematic study of estimation capacity, a criterion of model robustness, under the absence of interactions involving three or more factors. Some general results, providing designs with maximum estimation capacity, are obtained. In particular, for two-level factorials, it is seen that constructing a design with maximum estimation capacity calls for choosing points from a finite projective geometry such that the number of lines is maximized and the distribution of these lines among the chosen points is as uniform as possible. We also explore the connection with minimum aberration designs under which the sizes of the alias sets of two-factor interactions which are not aliased with main effects are the most uniform possible.