Optimizing two-level orthogonal arrays for simultaneously estimating main effects and pre-specified two-factor interactions

This paper considers the construction of D-optimal two-level orthogonal arrays that allow for the joint estimation of all main effects and a specified set of two-factor interactions. A sharper upper bound on the determinant of the related matrix is derived. To numerically obtain D-optimal and nearly D-optimal orthogonal arrays of large run sizes, an efficient search procedure is proposed based on a discrete optimization algorithm. Results on designs of 20, 24, 28, 36, 44 and 52 runs with three or fewer two-factor interactions are illustrated here to demonstrate the performance of the proposed approach. In addition, two cases with four two-factor interactions are also demonstrated here.