Optimal orthogonal block designs for three-component symmetric general blending models in mixture experiment

In mixture experiments, the observed response is determined by the relative proportions of the components, consequently rendering the experimental region a simplex. This paper focuses primarily on the optimal designs of mixture experiments that involve process variables. Prior research has extensively delved into optimal orthogonal block designs for some classic mixture models with process variables. Based on the framework of general blending models, this paper proposes a class of symmetric linear mixture models, which can be regarded as a generalization of many existing ones. Under the orthogonal blocking conditions, orthogonal block designs are devised through Latin squares in the presence of process variables. The D-, A-, and E-optimality criteria are utilized to obtain optimal designs at the boundary of the simplex in the case of 3 components. As the values of the exponents change, numerically derived optimal design points are presented to illustrate the pattern of their variations, and to verify the consistency of the results with previous research on some specific symmetric general blending models.