Blocked regular fractional factorial designs with maximum estimation capacity

In this paper, the problem of constructing optimal blocked regular fraction al factorial designs is considered. The concept of minimum aberration due t o Fries and Hunter is a well-accepted criterion for selecting good unblocke d fractional factorial designs. Cheng, Steinberg and Sun showed that a mini mum aberration design of resolution three or higher maximizes the number of two-factor interactions which are not aliases of main effects and also ten ds to distribute these interactions over the alias sets very uniformly. We extend this to construct block designs in which (i) no main effect is alias ed with any other main effect not confounded with blocks, (ii) the number o f two-factor interactions that are neither aliased with main effects nor co nfounded with blocks is as large as possible and (iii) these interactions a re distributed over the alias sets as uniformly as possible. Such designs p erform well under the criterion of maximum estimation capacity, a criterion of model robustness which has a direct statistical meaning. Some general r esults on the construction of blocked regular fractional factorial designs with maximum estimation capacity are obtained by using a finite projective geometric approach.