Orthogonal Arrays Robust to a Specified Set of Nonnegligible Effects

This paper considers experimental situations where the interested effects have to be orthogonal to a set of nonnegligible effects. It is shown that various types of orthogonal arrays with mixed strength are A-optimal for estimating the parameters in ANOVA high dimension model representation. Both cases including interactions or not are considered in the model. In particularly, the estimations of all main effects are A-optimal in a mixed strength (2, 2)₃ orthogonal array and the estimations of all main effects and two-factor interactions in G ₁×G ₂ are A-optimal in a mixed strength (2, 2)₄ orthogonal array. The properties are also illustrated through a simulation study.