Author(s): Cheruiyot Kipkoech, Koske Joseph and Mutiso John

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 be either on precise model estimation or precise predictions of responses. The main aim of I-optimality is to minimize the average prediction variance throughout the region of interest. Although mixtures experiments are usually intended to predict the response for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients, little research has been done on I-optimal third degree Kronecker designs. I-optimal designs were studied in order to predict the response(s) and the optimal formulations for all possible ingredients in the 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. Maximal parameters of interest for third degree Kronecker model were considered. The general equivalence theorem for I-optimality was used to test optimality of different mixture formulations. UWSCD was found to perform better than WSCD in terms of average prediction variance with most formulations satisfying general equivalent theorem for I-optimality.

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