Projections of Definitive Screening Designs by Dropping Columns: Selection and Evaluation

Abstract

Abstract–Definitive screening designs permit the study of many quantitative factors in a few runs more than twice the number of factors. 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 superfluous 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 (sDSD) exists for m factors. In these cases, it is common practice to arbitrarily drop the last columns of the larger design. In this article, we show that certain statistical properties of the resulting experimental design depend on the exact columns dropped and that other properties are insensitive to these columns. We perform a complete search for the best sets of 1–8 columns to drop from sDSDs 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 small, or even nonexistent.

Keywords:

• Conference matrix
• D-efficiency
• Isomorphism
• Second-order model
• Two-factor interaction

Supplementary Material

Supplementary sections.pdf Details on the simulation protocol and results; discussion and derivations of design properties; and table with detailed results about dropping from 1-8 columns from sDSDs.

Supplementary files.zip Simulation protocol and programs to identify the best sets of columns to drop from sDSDs.

Additional information

Funding

The research that led to this article was financially supported by the Flemish Fund for Scientific Research FWO.