Abstract
This study presents an investigation of an optimal slope design in the second degree Kronecker model for mixture experiments in four dimensions and its application in blending of selected fruits to prepare punch. The study centers around weighted centroid designs, with the second degree Kronecker model. This is guided by the fact that the class of weighted centroid designs is a complete class in the Kiefer Ordering. To overcome the problem of estimability, a concise coefficient matrix is defined that aid in selecting a maximal parameter subsystem for the Kronecker model. The information matrix of the design is obtained using a linear function of the moment matrices for the centroids and directly linked to the slope matrix. The discussion is based on Kronecker product algebra which clearly reflects the symmetries of the simplex experimental region. From the family of matrix means, a well-defined function is used to determine optimal values of the efficient developed design. Finally, a demonstration is provided for the case where the design is applied in fruit blending.
Highlights
This study explores the response surface with the intent of obtaining the optimal response
The response of interest is considered as a function of a set of independent factors. In this response surface methodology (RSM) problem we assume a response of interest is influenced by four factors with the intent of optimizing this response
Pukelsheim, F., 2000), showed that the class of weighted centroid designs is a complete class for the Kiefer ordering
Summary
This study explores the response surface with the intent of obtaining the optimal response. The response of interest is considered as a function of a set of independent factors. In this response surface methodology (RSM) problem we assume a response of interest is influenced by four factors with the intent of optimizing (obtaining maximal value of) this response. The response in linked to the factors through a second degree polynomial model. In this mixture experiment the response is a function of the proportions of each ingredient. Let xi represent the proportion of the ith ingredient in the mixture. The experimental region for this mixture problem is a three dimensional simplex
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