Blocking schemes for definitive screening designs

In earlier work, Jones and Nachtsheim proposed a new class of screening designs called definitive screening designs. As originally presented, these designs are three-level designs for quantitative factors that provide estimates of main effects that are unbiased by any second-order effect and require only one more than twice as many runs as there are factors. Definitive screening designs avoid direct confounding of any pair of second-order effects, and, for designs that have more than five factors, project to efficient response surface designs for any two or three factors. Recently, Jones and Nachtsheim expanded the applicability of these designs by showing how to include any number of two-level categorical factors. However, methods for blocking definitive screening designs have not been addressed. In this article we develop orthogonal blocking schemes for definitive screening designs. We separately consider the cases where all of the factors are quantitative and where there is a mix of quantitative and two-level qualitative factors. The schemes are quite flexible in that the numbers of blocks may vary from two to the number of factors, and block sizes need not be equal. We provide blocking schemes for both fixed and random blocks. Supplementary materials for this article are available online.