To avoid multicollinearity in regression analysis, Ye and Zhou(2013) proposed $K-$optimality criterion. By far the most popular models for modeling the response of a mixture experiment are the Scheff\'{e} models. However, there have been no reports about constructing $K-$optimal designs for mixture models. The paper constructs $K-$optimal designs for first-order and second-order Scheff\'{e} models. The analytical solutions for first-order and second-order Scheff\'{e} models are obtained. A series of numerical results and examples are given to illustrate the theory.
翻译:为了避免回归分析中的多曲线性,Ye和Zhou(2013年)提出了美元-美元最佳标准。迄今为止,模拟混合物实验反应的最流行模型是Scheff\'{e}模型。然而,没有关于为混合物模型建造美元-美元最佳设计的报告。纸张为一阶和二阶Scheff\'{e}模型构建了美元-美元最佳设计。获得了第一阶和二阶Scheff\'{e}模型的分析解决方案。提供了一系列数字结果和实例来说明理论。