D- and A-optimal designs for multi-response mixture experiments with qualitative factors

Mixture experiments are widely used in industry, agriculture, food manufacturing, medicine, and other fields, especially in the pharmaceutical field, which has played an indispensable role in recent years. Most predecessors focused on analyzing the single response problem for discussing mixture experiments, and the research of mixture experiments with qualitative factors is even less. Unlike previous studies, this article considers the optimal design problem of a class of multi-response mixture models with qualitative factors. It gives the general expression of the information matrix, D- and A-criterion functions of the multi-response second-order Scheffé central polynomial model with different mixture components. The variance function is derived under the corresponding optimality criterion, and finally, we conduct a comparative analysis of the relative efficiency of two optimal designs.