Abstract
This study presents an investigation of an optimal slope design in the second degree Kronecker model for mixture experiments in three dimensions. The study is restricted to weighted centroid designs, with the second degree Kronecker model. A well-defined coefficient matrix is used to select a maximal parameter subsystem for the model since its full parameter space is inestimable. 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. Eventually the matrix means are used in determining optimal values of the efficient developed design.
Highlights
This study presents an investigation of an optimal slope design in the second degree Kronecker model for mixture experiments in three dimensions
The study is restricted to weighted centroid designs, with the second degree Kronecker model
The discussion is based on Kronecker product algebra which clearly reflects the symmetries of the simplex experimental region
Summary
This study deals with the exploration and optimization of response surface This is a problem faced by experimenters in many technical fields, where in general the response of interest is affected by a set of independent factors. In this response surface methodology (RSM) problem we assume a response of interest is influenced by three factors with the intent of optimizing 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. The experimental region for the mixture problem is a two dimensional simplex
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