Optimal Designs For Mixture Experiments With Multidimensional Linear Models And Classification Models

Mixture design is an optimization problem in irregular regions,which is based on the theory of optimal design.It is widely used in biology,medicine,agriculture and economy.In this research field,there are many research hotspots about the optimal design under the different optimal criteria and different models.This paper mainly discusses the optimal design under the multidimensional linear model and the classification models with qualitative factors.In many practical cases,there is not only one response variable.We often have to consider that the model contains more than one response variable.Using the vector transformation method to transform the Multidimensional linear mixture model into one dimensional form in two situations of grouping and non group-ing.Further more,according to the result of mean inequality and the ?- optimal design theorem,we obtain the conclusion that when a design (?)* is ?- optimal in one dimensional linear mixture model,then (?)* is also ?- optimal under the multidimensional models in two situations of grouping and non grouping.The response of mixture classification model with qualitative factors is affect-ed by the two part of control variables.Some control variables are affected by qualitative factors,while the other is not affected by qualitative factors.Based on the theory of optimal design,the variance functions of D-?A- and R- criterion are derived,and it is proved that the uniform design of ?~* on{1,2,···,s} is the necessary condition to achieve the optimal for the mixture classification model.The example of common mixture polynomial model and its simulation verification are also given.Finally,we summarize the main contents and introduce the further work.