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Abstract:
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Jones and Nachtsheim (2011) introduced a class of three-level screening designs called definitive screening designs (DSDs). The structure of these designs results in the ability to estimate all quadratic effects. Thus, DSDs can allow for the screening and optimization of a system in one step, provided the number of active effects is less than about half the number of runs (Errore et al., 2017). Otherwise, estimation of second-order models requires augmentation of the DSD. In this paper, we focus on augmenting DSDs for the precise estimation of a response of interest when the correct form of the model for that response is quadratic. We explore series of augmented designs, moving from the starting DSD to designs comparable in sample size to central composite designs. We perform a simulation study to consider predicted mean square error of the designs and determine the number of augmented runs required for precise prediction of the response. We find that little is gained by augmenting beyond the design that is saturated for the full quadratic model. Surprisingly, augmentation strategies based on the D-optimality criterion are superior to strategies based on the I-optimality criterion.
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