I-optimal Designs for three and four component mixture models in orthogonal blocks

Abstract

In Industrial and Pharmaceutical experiments it is desired to have best predictions of the response on the basis of small amount of data.  Mixture experiment generally aims to predict the response(s) for all possible mixture blends. When we compute optimal design for mixture response surface we must focus on prediction capability of the design. The conventional optimal criteria, such as D-, A- and E-optimality are not suitable for determining the prediction capability of designs. As I-optimal design minimizes the average variance of prediction over the mixture region, so it clearly focuses on prediction capability of the design. Hence I-optimal criterion seems to be more appropriate in this conjecture.  In this paper we propose the construction of I-optimal mixture designs for a quadratic Scheffé’s and Darroch and Waller’s model in three and four components, using two orthogonal blocks.  I-efficiency of designs is compared with the I-efficiency of D-optimal designs for Scheffé’s and Darroch and Waller’s models.