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

Abstract

We consider a fractional 2^m₁+m₂ 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 m_k ≥ 2 (k = 1, 2). In this paper, we give a necessary and sufficient condition for an SPBA to be a partially balanced fractional 2^m₁+m₂ 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.