Extensions of D-optimal minimal designs for symmetric mixture models. Issue 5 (4th March 2017)

• Record Type: Journal Article
• Authors: Li, Yanyan; Raghavarao, Damaraju; Chervoneva, Inna
• Is Part Of: Communications in statistics. Volume 46:Issue 5(2017)
• Page Start: 2542
• Page End: 2558
• Publication Date: 2017-03-04
• Subjects: D-optimal minimal design -- Interior design points -- Lack of fit -- Mixture models.; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.988258
• Languages: English
• ISSNs: 0361-0926

Abstract

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 ) two 10-point designs for the LOF test by simulations.