Three-level designs: Evaluation and comparison for screening purposes

Since their introduction by Box and Hunter, resolution criteria have been widely used when comparing regular fractional factorials designs. In this article, we investigate how a generalized resolution criterion can be used to assess some recently developed three-level screening designs, such as definitive screening designs (DSDs) and screening designs from weighing matrices. The aim of this paper is to capture the projection properties of those three-level screening designs, complementing the work of Deng and Tang, who used generalized resolution and minimum aberration criteria for ranking different two-level designs, particularly Plackett-Burman and other nonregular factorial designs. An advantage of generalized resolution, extended here to work on three-level designs, is that it offers a useful criterion for ranking three-level screening designs, whereas the Deng and Tang resolution is used mainly for the assessment of two-level designs. In addition, we applied a projection estimation capacity (PEC) criterion to select three-level screening designs with desirable properties. Practical examples and the best projections of the designs are presented in tables.