GA-optimal partially balanced fractional $2^{m_1+m_2}$ factorial designs of resolution ${R}(\{00,10,01\}|\Omega)$} with $2\leq m_1,m_2 \leq 4$

Abstract

Under the assumption that the three-factor and higher-order interactions are negligible, we consider a partially balanced fractional $2^{m_1+m_2}$ factorial design derived from a simple partially balanced array such that the general mean, all the $m_1+m_2$ main effects, and some linear combinations of $\binom{m_1}{2}$ two-factor interactions, of the $\binom{m_2}{2}$ ones and of the $m_1m_2$ ones are estimable, where $2\leq m_k$ for $k=1,2$. This paper presents optimal designs with respect to the generalized A-optimality criterion when the number of assemblies is less than the number of non-negligible factorial effects, where $2\leq m_1, m_2 \leq 4$.