Augmenting definitive screening designs: Going outside the box

Definitive screening designs (DSDs) have grown rapidly in popularity since their introduction by Jones and Nachtsheim (2011 Jones, B., and C. J. Nachtsheim. 2011. A class of three-level designs for definitive screening in the presence of second-order effects. Journal of Quality Technology 43 (1):1–15. doi: 10.1080/00224065.2011.11917841.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Their appeal is that the second-order response surface (RS) model can be estimated in any subset of three factors, without having to perform a follow-up experiment. However, their usefulness as a one-step RS modeling strategy depends heavily on the sparsity of second-order effects and the dominance of first-order terms over pure quadratic terms. To address these limitations, we show how viewing a projection of the design region as spherical and augmenting the DSD with axial points in factors found to involve second-order effects remedies the deficiencies of a stand-alone DSD. We show that augmentation with a second design consisting of axial points is often the Ds-optimal augmentation, as well as minimizing the average prediction variance. Supplemented by this strategy, DSDs are highly effective initial screening designs that support estimation of the second-order RS model in three or four factors.