Optimal Design For Mixture Experiment With Correlation

As one of the experimental design,the mixture experiment design mainly studies optimal design problem in irregular region.It is widely used in producing food,medicine,sinter,polymer plastic and other products.The optimal design of different mixture models under different optimal criteria is usually studied.This paper mainly discusses the optimal design of mixture models with correlation and semi-variable coefficient.The mixture regression model is generally used in the mixture experiment and includes two main influencing factors,the random error factor and regression coefficient factor.The random error of mixture model is usually assumed to be constant variance,but there are often correlation in the actual experiment,which variance of random error is not fixed.It is significant to study the mixture model with correlation.The mixture model with correlation is studied,and its informa-tion matrix,kernel function and theorem of the decision function and supremum function under the criterion function are studied.Then the decision theorem of D-optimal,A-optimal and G-optimal design are solved.With the development of nonlinear mixture model,the mixture model with semi-variable coefficient,is different from linear regression model lies in its partial coefficient uncertainty.In the case of complex data such as measurement error data or missing data,it is great significance to study the mixture model with semi-variable coefficient.The first-order semi-variable coefficient mixture model is studied,and is transformed into mixed effect model.Then the information matrix of the model is obtained,and the D-optimal,V-optimal and G-optimal designs of the model are calculated.Finally,we summarizes the main content and innovation points of research,and introduce the future work.