Construction and selection of the optimal balanced blocked definitive screening design

The definitive screening (DS) design was proposed recently. This new class of three-level designs provides efficient estimates of main effects that are unaliased with any second-order effects. For practical use, we further study the optimal scheme for blocking DS designs. We propose a construction method and utilize the blocked count function to select the optimal balanced blocked definitive screening (BBDS) design in terms of generalized minimum aberration. The proposed BBDS design not only inherits properties of the original DS design but also guarantees that main effects are unconfounded by block effects. Besides that, it has minimum run size and is a saturated design for estimating the mean, all block effects, all main effects, and all quadratic effects.