K-optimal designs for the second-order Scheffé polynomial model

The K-optimality criterion is proposed to avoid multicollinearity in regression analysis. By far the most, popular models for modeling the response of a mixture experiment are the Scheffé polynomial models. The Scheffé polynomial models have a small degree of multicollinearity. However, there have been no reports about constructing K-optimal designs for the Scheffé polynomial models. This article expands the K-optimality criterion to the second-order Scheffé polynomial model, and derives the K-optimal allocations for such model. We also investigate the construction method of K-optimal designs with the non linear constraints. In addition, the relative efficiencies of D-, A-, and K-optimal designs are compared.