Projections of definitive screening designs by dropping columns: Selection and evaluation

Definitive screening designs are increasingly used for studying the impact of many quantitative factors on one or more responses in relatively few experimental runs. In practical applications, researchers often require a design for m quantitative factors, construct a definitive screening design for more than m factors and drop the super uous columns. This is done when the number of runs in the standard m-factor definitive screening design is considered too limited or when no standard definitive screening design exists for m factors. In these cases, it is common practice to arbitrarily drop the last column of the larger definitive screening design. In this paper, we show that certain statistical properties of the resulting experimental design depend on which columns are dropped and that other properties are insensitive to the exact columns dropped. We perform a complete search for the best sets of 1-8 columns to drop from standard definitive screening designs with up to 24 factors. We observed the largest differences in statistical properties when dropping four columns from 8- and 10-factor definitive screening designs. In other cases, the differences are moderate or small, or even nonexistent. Our search for optimal columns to drop necessitated a detailed study of the properties of definitive screening designs. This allows us to present some new analytical and numerical results concerning definitive screening designs.