434 research outputs found
Extensions of D-optimal Minimal Designs for Symmetric Mixture Models.
The purpose of mixture experiments is to explore the optimum blends of mixture components, which will provide desirable response characteristics in finished products. D-optimal minimal designs have been considered for a variety of mixture models, including Scheffé\u27s 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 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 PAPER 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 ten-point designs for the Lack of Fit test by simulations
Universal optimality of Patterson's crossover designs
We show that the balanced crossover designs given by Patterson [Biometrika 39
(1952) 32--48] are (a) universally optimal (UO) for the joint estimation of
direct and residual effects when the competing class is the class of connected
binary designs and (b) UO for the estimation of direct (residual) effects when
the competing class of designs is the class of connected designs (which
includes the connected binary designs) in which no treatment is given to the
same subject in consecutive periods. In both results, the formulation of UO is
as given by Shah and Sinha [Unpublished manuscript (2002)]. Further, we
introduce a functional of practical interest, involving both direct and
residual effects, and establish (c) optimality of Patterson's designs with
respect to this functional when the class of competing designs is as in (b)
above.Comment: Published at http://dx.doi.org/10.1214/009053605000000723 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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