Bayesian Approach to the D-Optimal for Mixture Experimental Design

Abstract

A mixture experiment is a special case of response surface methodology in which the value of the components are proportions. In case there are constraints on the proportions, the experimental region can be not a simplex. The classical designs such as a simplex-lattice design or a simplex-centroid design, in some cases, cannot fit to the problem. In this case, optimal design come up as a solution. A D-optimal design is seeking a design in which minimizing the covariance of the model parameter. Some model parameters are important and some of them are less important. As the priority of the parameters, the prior information of parameters is needed in advance. This brings to a Bayesian D-optimal design. This research was focus on a baking experiment in which consisted of three ingredients with lower bounds on the proportion of the ingredients. The assumption model was a quadratic model. Due to the priority of the model parameters, the Bayesian D-optimal design was used to solve the problem. A point-exchange algorithm was developed to find the optimal design. Nineteen candidates is used to choose twelve design points. It found that the potential term is feasible to the actual model and design points represent overall points in the design area.