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Volume 6, Issue 4, July 2017, Page: 170-175
Slope Optimal Designs for Third Degree Kronecker Model Mixture Experiments
Cheruiyot Kipkoech, Department of Mathematics and Physical Sciences, Maasai Mara University, Narok, Kenya
Koske Joseph, Department of Statistics and Computer Science, Moi University, Eldoret, Kenya
Mutiso John, Department of Statistics and Computer Science, Moi University, Eldoret, Kenya
Received: Oct. 13, 2016;       Accepted: Oct. 28, 2016;       Published: Jun. 1, 2017
DOI: 10.11648/j.ajtas.20170604.11      View  1963      Downloads  96
Abstract
Mixture experiments are special type of response surface designs where the factors under study are proportions of the ingredients of a mixture. In response surface designs the main interest of the experimenter may not always be in the response at individual locations, but the differences between the responses at various locations is of great interest. Most of the studies on estimation of slope (rate of change) have concentrated in Central Composite Designs (CCD) yet mixture experiments are intended to show the response for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients at different locations. Slope optimal mixture designs for third degree Kronecker model were studied in order to obtained optimal formulations for all possible ingredients in simplex centroid. Weighted Simplex Centroid Designs (WSCD) and Uniformly Weighted Simplex Centroid Designs (UWSCD) mixture experiments were obtained in order to identify optimal proportions for each of the ingredients formulation. Derivatives of the Kronecker model mixture experiment were used to obtain Slope Information Matrices (SIM) for four ingredients. Maximal parameters of interest for third degree Kronecker model were considered. D-, E-, A-, and T- optimal criteria and their efficiencies for both WSCD and UWSCD third degree Kronecker model were obtained. UWSCD was found to be more efficient than WSCD for almost all the points in the simplex designs, therefore recommended for more optimal results in mixture experiments.
Keywords
Kronecker Model, Optimal Designs, Slope Information Matrices (SIM), Weighted Simplex Centroid Designs, A-, D-, E- and T-Optimality
To cite this article
Cheruiyot Kipkoech, Koske Joseph, Mutiso John, Slope Optimal Designs for Third Degree Kronecker Model Mixture Experiments, American Journal of Theoretical and Applied Statistics. Vol. 6, No. 4, 2017, pp. 170-175. doi: 10.11648/j.ajtas.20170604.11
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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