基于二阶指数混料模型的A-最优设计

A-optimal Design for Second-order Exponential Mixture Model

使用最优设计理论研究混料试验的过程中,需考虑混料模型对应的函数向量。当函数向量为非线性函数时,虽可使用Taylor级数进行近似,但级数阶的选取必然使得误差的存在,给试验带来偏差。本文旨在使用最优设计理论,研究q分量二阶指数混料模型的A-最优设计问题,并得到了该模型下的最优设计。且从设计效率的角度,研究了不同分量下的A-最优设计效率,为确定设计优劣提供了一个依据,并给出了进一步可以研究的问题。

In the study of the mixture experiments,the optimal design theory should consider the function vector corresponding to the mixture model.However,when the function vector is a nonlinear function,Taylor series is used for approximation.The selection of series order makes certain errors,which leads to deviations in the experiment.In this paper,we study the A-optimal design of the q-components second-order exponential mixture model by using the optimal design theory,and obtain the optimal design under the model.At last,we find the A-optimal design efficiency for different components,which provides a method for determining the design quality.