Ga-optimal partially balanced fractional2m1+m2 factorial designs of resolutions r({10,01}∪Ω* | Ω) with 2 ≤ m1, m2 ≤ 4

We consider a partially balanced fractional 2 1 2m1 +m2 factorial design derived from a simple partially balanced array such that all the 1 m main effects (=q10, say) and all the m2 ones (= q01, say) are estimable, and in addition that the general mean (=q00, say) is at least confounded (or aliased) with the factorial effects of the (Formula Presented) two-factor interactions (=q20, say), the (Formula Presented) ones (=q02, say) and/or the 1 2 m1 m2 ones (=q11, say), where the three-factor and higher-order interactions are assumed to be negligible, and 2 k ≤ mk for k = 1,2. Furthermore optimal designs with respect to the generalized A-optimality criterion are presented for 2 ≤ m1, m2 ≤ 4when the number of assemblies is less than the number of non-negligible factorial effects. © 2007 Taylor & Francis Group, LLC. All rights reserved.