Open AccessA- Optimal Slope Design for Second Degree Kronecker Model Mixture Experiment With Four Ingredients With Application in Selected Fruits Blending
Author(s) -
Ngigi Peter Kung’u,
J. K. Koske,
Josphat K. Kinyanjui
Publication year - 2021
Publication title -
international journal of statistics and probability
Language(s) - English
Resource type - Journals
eISSN - 1927-7040
pISSN - 1927-7032
DOI - 10.5539/ijsp.v10n2p36
Subject(s) - kronecker delta , kronecker product , mathematics , centroid , simplex , degree (music) , matrix (chemical analysis) , class (philosophy) , function (biology) , product (mathematics) , pure mathematics , combinatorics , computer science , geometry , physics , materials science , quantum mechanics , artificial intelligence , evolutionary biology , acoustics , composite material , biology
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.