Extensions of D-optimal minimal designs for symmetric mixture models |
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Authors: | Yanyan Li Damaraju Raghavarao Inna Chervoneva |
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Affiliation: | 1. Department of Statistics, CSL Behring Biotherapies for Life, King of Prussia, PA, USA;2. Department of Statistics, Temple University, Philadelphia, PA, USA;3. Department of Pharmacology and Experimental Therapeutics, Thomas Jefferson University, Philadelphia, PA, USA |
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Abstract: | The purpose of mixture experiments is to explore the optimum blends of mixture components, which will provide the desirable response characteristics in finished products. D-optimal minimal designs have been considered for a variety of mixture models, including Scheffé's linear, quadratic, and cubic models. Usually, these D-optimal designs are minimally supported since they have just as many design points as the number of parameters. Thus, they lack the degrees of freedom to perform the lack-of-fit (LOF) tests. Also, the majority of the design points in D-optimal minimal designs are on the boundary: vertices, edges, or faces of the design simplex. In this article, extensions of the D-optimal minimal designs are developed for a general mixture model to allow additional interior points in the design space to enable prediction of the entire response surface. Also a new strategy for adding multiple interior points for symmetric mixture models is proposed. We compare the proposed designs with Cornell (1986 Cornell, J.A. (1986). A comparison between two ten-point designs for studying three-component mixture systems. J. Qual. Technol. 18(1):1–15.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) two 10-point designs for the LOF test by simulations. |
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Keywords: | D-optimal minimal design Interior design points Lack of fit Mixture models. |
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