几类含定性因子的复合型混料模型的I-最优设计

I-optimal design of mixture models with a qualitative factor

混料试验是一种研究对象为混料成分比例的试验.在混料试验中,当响应变量受到分类变量影响时,需要建立一类含有定性因子的复合型混料模型,以对实际试验设计问题进行拟合.在一般的最优试验设计问题中,良好的预测特性对于优化至关重要,I-最优设计则是一类重要的基于预测的试验设计.文章旨在研究含定性因子混料模型的I-最优设计,给出该类混料模型的I-最优相关定理,并对三种常见混料模型在含有定性因子的情况下进行近似I-最优配置的求解,最终得到可应用于实际生产生活的结论.

The mixture experiment is a kind of experiment whose aim is to study the proportion of mixture components. In the mixture experiment, if the response is also affected by the categorical variable, a type of compound mixture model containing qualitative factors should be established to fit the actual experimental design problem. In general optimum experimental design problems, good prediction properties are essential for optimization. I-optimal design is an important prediction-based experimental design. The purpose of this paper is to study the I-optimal design of mixture models with a qualitative factor, to give some theorems for I-optimal of this kind of mixture model, as well as to calculate the approximate I-optimal weights of three basic mixture models with a qualitative factor. The derived conclusions at the end of this article can be applied to actual life.