Study On D-、E-optimal Mixture Experiment Designs Of Several Models

Mixture experimental design is devoted to the study of the optimal formulation of mixture ingredients.It is widely used in food science,industrial product manufacturing and biomedicine.How to find a scientific design scheme that can save manpower,material and financial resources according to the purpose of the experiment,based on appropriate models and specific optimality criteria,which is worthy of our in-depth discussion.At present,most of the literatures on mixture experiment is based on "standard mixture models" such as the Scheffé canonical polynomial model,and most of them only investigated the common optimal design problems of the models,with relatively little research on special mixture models and other optimal designs.In this paper,we consider the D-optimal and E-optimal design problems for the following types of mixture models.Firstly,in the case of a mixture system where some of the mixture components exhibit linear additivity effects and the remaining components exhibit non-linear mixing effects,and where the support points are to be determined,a special class of mixture exponential model is proposed,and the support points of this model are searched for in the whole simplex factor space through the interior point method and the graph check method,and finally,the D-optimal design of the model is calculated and proved by the equivalence theorem.Secondly,the E-optimal design uses the idea of a game to control the maximum variance of the parameter estimates to a minimum,which in turn brings the parameter to be estimated closer to the true value.It makes up for some of the deficiencies of the optimality criteria represented by D-,G-,etc.in considering the confidence ellipsoid properties of the parameter estimates,so this paper investigates the E-optimal design problems for the q-component Scheffe central polynomial model.This part of the paper focuses on using the theoretical knowledge of E-optimal design to determine the explicit expressions for both the E-criterion function and the E-optimal design of this model,and thus the analytic solution of the E-efficiency obtained.Finally,an example is given to compare the advantages and disadvantages of the E-,D-and A-optimal designs from an efficiency point of view.Finally,based on the above discussion,a summary of the full text is presented as well as an outlook for future research work.