Definitive Screening Design (DSD): Characteristics and Analysis Methods

DSDs require a more thoughtful approach to the analysis than is typical for other designs produced by the software. The word “screening” in the name of the design implies that they are intended to find factors with significant linear effects. Because they are built with three levels of all the numeric factors, there are limited circumstances where a good approximation of the true response surface can be found.

The concept of screening is that there are too many factors of interest to fit the full quadratic polynomial model; it would take too many runs. Instead, a design is used that is capable of fitting all of the linear terms, and possibly some of the two-factor interactions and quadratic terms (second-order model).

Only factors with unknown effects should be included in the screening design. It is best to hold factors with known effects out until a later phase of the experiment. Leaving out known factors reduces the number of runs required in the screening design, and will reduce the number of important effects that need to be estimated. The unknown factors that show significant and substantial linear effects are re-combined with the known factors in a more capable characterization or even optimization design.

DSDs have good properties for finding the significant linear effects, regardless of active second-order effects. Significant linear effects are more readily identified with factorial screening designs (i.e. Resolution IV regular factorials, and Min Run Screening) because they have somewhat higher power for the linear model than a similarly sized DSD. One way to increase the power of a DSD is to build the design with at least two extra numeric factors, then delete the columns that aren’t needed for a real factor.

What separates the DSDs from factorial screening designs, and the reason they are on the response surface tab in Stat-Ease, is their ability to fit unaliased subsets of the second-order model terms. The subsets can have no more than three active factors. When there are three or fewer active factors, a DSD might be able to provide a shortcut to go directly from screening to finding optimized settings.

The software’s default analysis starts with the full quadratic model and a recommendation to reduce the number of terms to an unaliased subset. This can be done by either manually picking terms or by using the Automatic Selection algorithm. If there are more than three factors active among the second-order effects, then the aliasing present in DSDs may produce a meaningless model.

A more conservative model can be chosen from only the linear effects. Estimates of linear coefficients are unbiased by other linear or second-order effects. As with any screening analysis, the factors with linear effects can be examined more thoroughly in the next phase of experimentation.

A safe approach when analyzing DSDs is to treat significant second-order effects as evidence to augment the design to fit a model including the two-factor interactions and quadratic terms. Click the Design Tools menu, select Augment Design, and then Augment to add optimal runs to the design.

Click here for more information on augmenting a design.