GA-optimal Partially Balanced Fractional 2^m1+m2 Factorial Designs of Resolutions R({10,01} ∪ Ω* | Ω) with 2 ≤ m₁, m₂ ≤ 4

Abstract

We consider a partially balanced fractional 2^m1+m2 factorial design derived from a simple partially balanced array such that all the m₁ main effects (= θ₁₀, say) and all the m₂ ones (= θ₀₁, say) are estimable, and in addition that the general mean (= θ₀₀, say) is at least confounded (or aliased) with the factorial effects of the (2 m₁) two-factor interactions (= θ₂₀, say), the (2 m₂) ones (= θ₀₂, say) and/or the m₁m₂ ones ( = θ₁₁, say), where the three-factor and higher-order interactions are assumed to be negligible, and 2 ≤ m_k for k = 1,2. Furthermore optimal designs with respect to the generalized A-optimality criterion are presented for 2 ≤ m₁,m₂ ≤ 4 when the number of assemblies is less than the number of non-negligible factorial effects.