Definitive screening designs require only a small number of runs, use three levels of continuous factors, and allow for the estimation of main effects as well as some interaction and quadratic terms. Investigators use screening designs when they want to identify the factors that have the most substantial effects on a response. A screening design enables you to study a large number of factors in a fairly small experiment.
Many standard screening designs focus on estimating main effects. Definitive screening designs offer advantages over standard screening designs. They avoid confounding of effects and can identify factors having a nonlinear effect on the response. For more information about the advantages and construction of definitive screening designs, see Jones and Nachtsheim (2011a).
For designs containing only continuous factors, compare these properties of definitive screening designs versus standard screening designs:
Note: When quadratic effects are mentioned, the standard screening designs are assumed to have center points.
• Main effects are orthogonal to two-factor interactions.
– Definitive Screening Designs: Always
– Standard Screening Designs: Only for Resolution IV or higher
• No two-factor interaction is completely confounded with any other two-factor interaction.
– Definitive Screening Designs: Always
– Standard Screening Designs: Only for Resolution V or higher
• All quadratic effects are estimable in models containing only main and quadratic effects.
– Definitive Screening Designs: Always
– Standard Screening Designs: Never
These properties are described more fully in the remainder of this section.
Standard screening designs, such as fractional factorial or Plackett-Burman designs, attempt to study many factors with a relatively small allocation of resources. However, standard screening designs have several undesirable features:
• They can alias some main effects with two-factor interactions. In Plackett-Burman designs, for example, main effects are correlated with several two-factor interactions. If one or more two-factor interaction effects are substantial, then the experimenter must perform additional runs to resolve the ambiguities.
• They can also confound some two-factor interactions with each other. Consequently, if a two-factor interaction effect is substantial, then the experimenter must perform additional runs to resolve the remaining ambiguities.
• Continuous factors are usually set at only two levels (low and high). However, engineers and scientists often prefer designs where continuous factors are set at three levels (low, middle, and high). This is because two levels are not sufficient to detect nonlinearity, which is common in physical systems. You can use a traditional screening design with added center points to detect nonlinearity, but such a design does not identify the responsible factors.
Using definitive screening designs, you can do the following:
• Avoid model ambiguity, enabling you to identify important factors more quickly and efficiently.
• Identify the cause of nonlinear effects while avoiding confounding any terms up to second order. So not only can you detect nonlinearity, as you might with center points in a traditional screening design, but you can identify the responsible factors.
Definitive screening designs offer the following advantages:
• Definitive screening designs require only a small number of runs. For six or more factors, the minimum number of required runs is usually only a few more than twice the number of factors. For more detail about the number of runs, see Conference Matrices and the Number of Runs.
• Main effects are orthogonal to two-factor interactions. This means that estimates of main effects are not biased by the presence of active two-factor interactions, whether these interactions are included in the model or not. Note that resolution III screening designs confound some main and interaction effects. Also, Plackett-Burman designs produce biased main effect estimates if there are active two-factor interactions.
• No two-factor interaction is completely confounded with any other two-factor interaction. However, a two-factor interaction might be correlated with other two-factor interactions. Note that resolution IV screening designs completely confound some two-factor interaction effects.
• All quadratic effects are estimable in models comprised only of main effects and quadratic terms. This enables you to identify the factors that account for nonlinearity. Note that traditional screening designs with added center points do not allow estimation of all quadratic effects in models consisting of main and quadratic effects.
• Quadratic effects are orthogonal to main effects and not completely confounded with two-factor interactions. A quadratic effect might be correlated with interaction effects.
• For 6 through at least 30 factors, it is possible to estimate the parameters of any full quadratic model involving three or fewer factors with high precision.
• For 18 factors or more, they can fit full quadratic models in any 4 factors. For 24 factors or more, they can fit full quadratic models in any 5 factors.
The Definitive Screening Design platform enables you to construct definitive screening designs for continuous factors and for two-level categorical factors. It also enables you to construct blocked designs. You can add extra non-center runs to enhance the ability of the design to reliably detect effects when many effects are active.
To view the absolute values of the correlations among effects, use the Color Map on Correlations provided as part of the Design Evaluation section in the Definitive Screening Design window. You can compare the aliasing structure of definitive screening designs to that of other designs by comparing their color maps on correlations. See “Color Map on Correlations”.
For more information about the structure of definitive screening designs, see Structure of Definitive Screening Designs. For information about definitive screening designs with blocks, see Blocking in Definitive Screening Designs. For suggestions on how to analyze data obtained using definitive screening designs, see Analysis of Experimental Data.
After you run a Definitive Screening Design (DSD), analyze your results using the Fit Definitive Screening platform. Standard model selection methods applied to DSDs can fail to identify active effects. To identify active main effects and second-order effects, the Fit Definitive Screening platform uses an algorithm called Effective Model Selection for DSDs. This algorithm leverages the special structure of DSDs. See “The Fit Definitive Screening Platform”.
If you create your DSD in JMP, the design table contains a script called Fit Definitive Screening that automatically runs an analysis using the Effective Model Selection for DSDs methodology.