Characterization of Partially Balanced Fractional 2m1+m2 Factorial Designs of Resolution R({00, 10, 01, 11})

We consider a fractional 212 factorial design derived from a simple partially balanced array (SPBA), and we assume that the non-negligible factorial effects are the general mean, all the main effects and the two-factor interactions between the m1 factors and the m2 ones, and mk ≥ 2 (k = 1, 2). In this paper, we give a necessary and sufficient condition for an SPBA to be a partially balanced fractional 212 factorial design such that all the non-negligible factorial effects are estimable, whose design is said to be of resolution R({00, 10, 01, 11}). Such a design is concretely characterized by the suffixes of the indices of an SPBA.