Design and Analysis of Experiments with Mixtures

Murty, J. S.; Das, Moumita

doi:10.1214/aoms/1177698134

Cited by 48 publications

(21 citation statements)

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“…The number of design points required for selected fractional simplex designs versus a second-order simplex lattice are presented in Table 2. The resultant designs meet previously published requirements for symmetric mixture designs (Murty and Das, 1968). Designs meeting these symmetry requirements have associated statistical properties, such as equal variance estimates for main factors and for interaction terms in the mixture models presented in Section 3.…”

Section: Fractional Simplex Designsmentioning

confidence: 56%

Fractional Simplex Designs for Interaction Screening in Complex Mixtures

et al. 2000

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In mixture experiments, one may be interested in estimating not only main effects but also some interactions. Main effects and significant interactions in a mixture may be estimated through appropriate mixture experiments, such as simplex-centroid designs. However, for mixtures with a large number of factors, the run size for these designs becomes impractically large. A subset of a full simplex-centroid design may be used, but the problem remains regarding which factor-level settings should be selected. In this paper, we propose a solution that considers design points with either one or p individual nonzero factor-level settings. These fractional simplex designs provide a means of screening for interactions and of investigating the behavior of many-component mixtures as a whole while greatly reducing the run size compared with full simplex-centroid designs. The means of construction of the design arrays is described, and designs for < or = 31 factors are presented. Some of the proposed methodology is illustrated using generated data.

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Section: Fractional Simplex Designsmentioning

confidence: 56%

Fractional Simplex Designs for Interaction Screening in Complex Mixtures

et al. 2000

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“…For mixture models, commonly used designs include the simplex lattice design (Scheffé, 1958), the simplex centroid (Scheffé, 1963), the symmetric simplex design (Murty and Das, 1968) and the axial designs (Cornell, 1975). Their design points are mainly on the boundary: vertices, edges, or faces of design simplex.…”

Section: Introductionmentioning

confidence: 99%

Extensions of D-optimal minimal designs for symmetric mixture models

Raghavarao

Chervoneva

2016

Communications in Statistics - Theory and Methods

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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'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 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.

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“…The primary objective in using the polynomials (1.2) and (1.3) is one of fitting a response surface assuming the surface does not have discontinuities or other peculiarities a low degree polynomial cannot emulate. The simplex lattices and Scheffk's [lo] simplexcentroid designs are special cases of the more general class of symmetric-simplex designs introduced by Murty and Das [8].…”

Section: Introdxjcti~nmentioning

confidence: 99%

“…8) where in addition to the constraint (1.7), the q constraints are imposed g Pjksk = 0, for j = 1, 2, . .. , q.…”

Section: Introdxjcti~nmentioning

confidence: 99%