Journal ArticleDOI
Optimum Mixture Design Using Deficiency Criterion
Nripes Kumar Mandal,Manisha Pal +1 more
TLDR
In this paper, the deficiency criterion due to Chatterjee and Mandal (1981) has been used as a measure for comparing the performance of competing mixture models, and the problem of estimating the optimum proportion of mixture components is of great practical importance.Abstract:
In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe (1958, 1963) first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal (2006, 2007) attempted to find a solution to this problem by adopting a pseudo-Bayesian approach and using the trace criterion. Subsequently, Pal and Mandal (2008) solved the problem using minimax criterion. In this article, the deficiency criterion due to Chatterjee and Mandal (1981) has been used as a measure for comparing the performance of competing designs.read more
Citations
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Journal ArticleDOI
A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models
TL;DR: A projection based PSO technique is introduced, named ProjPSO, to efficiently find different types of optimal designs, or nearly optimal Designs, for mixture models with and without constraints on the components, and also for related models, like the log contrast models.
Journal ArticleDOI
NiO, Fe2O3, and MoO3 supported over SiO2 nanocatalysts for asphaltene adsorption and catalytic decomposition: Optimization through a simplex–centroid mixture design of experiments
Daniela Arias-Madrid,Oscar E. Medina,Jaime Gallego,Sócrates Acevedo,Alexander A. Correa-Espinal,Farid B. Cortés,Camilo A. Franco +6 more
TL;DR: In this paper, the effect of functionalized silica nanoparticles with Fe2O3, NiO, and MoO3 metal oxides on the decomposition of asphaltenes was evaluated through an experimental simplex-centroid mixture design for surface area, adsorption, and activation energy.
Optimum mixture designs under constraints on mixing components
TL;DR: In this article, Mandal et al. derived a pseudo-Bayesian approach with invariance property of the second order moments of the optimum mixing proportions for estimating the optimum proportion of mixture components when the factor space is constrained.
Journal ArticleDOI
Optimum Designs for Parameter Estimation in Linear Mixture Models with Synergistic Effects
TL;DR: In this article, the authors derived optimum designs for parameter estimation in a mixture experiment when the response function is linear in the mixing components with some synergistic effects using the equivalence theorem.
Journal ArticleDOI
Optimum mixture designs in a restricted region
TL;DR: In this paper, an ellipsoidal subspace of the entire factor space which does not cover the vertex points of the simplex is used as a support point of the optimum design.
References
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Journal ArticleDOI
Optimum Designs in Regression Problems
J. Kiefer,Jacob Wolfowitz +1 more
TL;DR: In this paper, the authors consider the problem of finding an optimum design of experiments in regression problems, where the desired inference concerns one of the regression coefficients, and illustrative examples will be given in Section 3.
Journal ArticleDOI
The Simplex-Centroid Design for Experiments with Mixtures
Henry Scheffé,Henry Scheffé +1 more
Journal ArticleDOI
Experiments with Mixtures
TL;DR: Experiments with Mixtures as discussed by the authors is a collection of experiments with mixtures written by J. A. Cornell and published by Wiley, Chichester, 1990. 632 pp.
Journal ArticleDOI
Optimal design: Variation in structure and performance under change of criterion
TL;DR: In this paper, the advisability of comparing designs on the basis of several different criteria of goodness is discussed, including A-, D- and E-optimality, as well as one of Box & Draper.