R-and Robust R-optimal Design Of Central Polynomial Mixture Model

Mixture experiment design mainly studies the experimental design problem in the formula ratio,which is a mathematical theory and method to arrange mixture experiment and analyze mixture data,and is an important branch of mathematical statistics.Mixture experiment design is an optimization problem in the constraint region,most of which is based on optimal design theory.It is widely used in industrial and agricultural production,management and scientific research,and has brought great economic and social benefits to enterprises and society.The optimal design problem based on different optimal criteria has always been a research hotspot in this field under different mixing models.In recent years,relevant researchers combine robust design with optimal design,and it has become a new research direction to discuss the robust optimal design of mixture model and regression model.Firstly,the R-optimal configuration of the second-degree central polynomial model is discussed by using R-optimal criterion theory,and the obtained optimal configuration is proved by using the equivalence theorem of R-optimal criterion.At the same time,this thesis discusses the R-optimal design problem of the third-degree central polynomial model of the concrete component,and gives the numerical solution of the R-optimal design of the three-component third-degree polynomial model by using Mathematica software.Secondly,based on the theory of robust R-optimal criterion,the robust R-optimal configuration of the second-degree central polynomial model is discussed,and the optimal configuration solution is obtained.For the specific prior measure,the robust R-optimal configuration of the three-component second-degree mixture model is given.Then,the robust R-optimal configuration is proved to be the robust R-optimal design by using the equivalence theorem of the robust R-criterion and the conditional extremum theorem of multivariate functions.Finally,the efficiency of R-optimal design and robust R-optimal design is compared and analyzed.