Volume 3, Issue 4, October 2017, Page: 86-91
Optimal Slope Designs for Second Degree Kronecker Model Mixture Experiments
Wambua Alex Mwaniki, Department of Planning and Statistics, Ministry of Agriculture, Livestock and Fisheries, Nairobi, Kenya
Njoroge Elizabeth, Department of Business Administration, Chuka University, Chuka, Kenya
Koske Joseph, Department of Mathematics and Computer Science, Moi University, Eldoret, Kenya
John Mutiso, Department of Mathematics and Computer Science, Moi University, Eldoret, Kenya
Kuria Joseph Gikonyo, Department of Mathematics, Statistics and Actuarial Sciences, Karatina University, Karatina, Kenya
Muriungi Robert Gitunga, Department of Mathematics, Meru University of Science and Technology, Meru, Kenya
Cheruiyot Kipkoech, Department of Mathematics and Physical Sciences, Maasai Mara University, Narok, Kenya
Received: Mar. 31, 2017;       Accepted: Apr. 14, 2017;       Published: Oct. 26, 2017
DOI: 10.11648/j.ijamtp.20170304.12      View  1886      Downloads  80
Abstract
The aim of this paper is to investigate some optimal slope mixture designs in the second degree Kronecker model for mixture experiments. The study is restricted to weighted centroid designs, with the second degree Kronecker model. For the selected maximal parameter subsystem in the model, a method is devised for identifying the ingredients ratio that leads to an optimal response. The study also seeks to establish equivalence relations for the existence of optimal designs for the various optimality criteria. To achieve this for the feasible weighted centroid designs the information matrix of the designs is obtained. Derivations of D-, A- and E-optimal weighted centroid designs are then obtained from the information matrix. Basically this would be limited to classical optimality criteria. Results on a quadratic subspace of H-invariant symmetric matrices containing the information matrices involved in the design problem was used to obtain optimal designs for mixture experiments analytically. The discussion is based on Kronecker product algebra which clearly reflects the symmetries of the simplex experimental region.
Keywords
Slope Mixture designs Kronecker product, Optimal Designs, Weighted Centroid Designs, A-, D-, E-Optimality and H- invariant Symmetric Matrices
To cite this article
Wambua Alex Mwaniki, Njoroge Elizabeth, Koske Joseph, John Mutiso, Kuria Joseph Gikonyo, Muriungi Robert Gitunga, Cheruiyot Kipkoech, Optimal Slope Designs for Second Degree Kronecker Model Mixture Experiments, International Journal of Applied Mathematics and Theoretical Physics. Vol. 3, No. 4, 2017, pp. 86-91. doi: 10.11648/j.ijamtp.20170304.12
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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