Type 1 optimal 2m fractional factorial plans with n l (mod 8) runs, l=1,2

This paper considers the issue of optimality of fractional factorial experiments involving m factors each at two levels. The optimality criteria used here is the type 1 criteria, due to Cheng (1978), which include the D- and A-criteria. It is shown that if there exists an orthogonal array OA(n - l, m, 2, 3), l = 1, 2, then there exists an n-run type 1 optimal fractional factorial plan for a 2(m) experiment under a model that includes the mean, all main effects and all two-factor interactions with a factor in common. These plans are obtained by adding any one run to an OA(n - 1, m, 2, 3) for n 1 (mod 8) and two specific runs to an OA(n - 2, m, 2,3) for n 2 (mod 8). (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.