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Abstract:
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Jones and Nachtsheim (2011) introduced a class of three-level screening designs subsequently called definitive screening designs (DSDs). The structure of these designs results in the statistical independence of best estimators for main effects and two-factor interactions; the absence of complete confounding among two-factor interactions; and the ability to estimate all quadratic effects. Because quadratic effects can be estimated, DSDs can allow for the screening and optimization of a system to be performed in one step, but only when the number of terms found to be active during the analysis of the data from the initial DSD is less than roughly half the number of runs required by the DSD. Otherwise, estimation of second-order models requires augmentation of the DSD. In this paper we explore the construction of a series of augmented designs, moving from the starting DSD to designs capable of estimating the full second-order model. We use power calculations and model-discrimination criteria to identify the numbers of augmented runs necessary to effectively identify a specified number of active model effects.
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