On optimal blocked definitive screening designs: Theoretical insights and computational simplifications

Definitive screening designs (DSDs) are a novel class of three-level designs that yield efficient estimates of main effects without aliasing with second-order effects. While orthogonal and pairwise blocking schemes have been proposed for DSDs, their theoretical properties remain partially unexplored, resulting in computational challenges in searching for optimal blocked DSDs. In this paper, we obtain several theoretical insights into optimal blocked DSDs under the linear-plus-quadratic effects model. Our results not only demonstrate the optimality of some existing blocked DSDs but also substantially alleviate the complexities involved in identifying optimal orthogonal blocked DSDs.