Study On Optimal Designs For Second-order Collapsed Mixture Model And The Cox Uniform Designs

We consider the influence of the proportion of each component on the response variable,not the influence of each component on the response variable in mixture experiment.The mixture experiment design has been developed over a long time,which forms two kinds of main thought:one is to set up the constrained region in the standard simplex region,and to construct the optimal design in the constrained region,called optimal design of mixture experiment;The other is to transform the uniform design in hypercube to standard simplex region,called uniform design of mixture experiment.In this paper,two works have done.Firstly,the optimal designs for secondorder collapsed mixture model is studied by combining the optimal design of mixture experiment.Secondly,I propose the Cox uniform design by combining Cox design,which overcomes the defects of the traditional Cox design on the lower order model,and it is a design that combines the optimal and the uniformity.So the model established in this method is more robust,an example is given to illustrate this method.This paper included five chapters:The first chapter,we introduce the research background and significance.The second chapter,we introduce systematically the basic theoretical of mixture experiment design.the problem of mixture experiment design,several typical mixture experiment design,classic optimal criteria and equivalence theorems,several methods to construct uniform design and deviations for measure the uniformity have introduced.The third chapter,using A-optimal design criteria and R-optimal equivalence theorem,-optimal design criteria and A-optimal equivalence theorem to study the second-order collapsed mixture model,obtain the R-optimal design and -optimal design of the model.The fourth chapter,using the theory of uniform design and Cox design to study the Cox uniform design of mixture experiment,the correlation theorem is used to prove that the D-optimal design in tne standard simplex region,which in Cox transform method can maintain the D-optimality in the subregion.The fifth chapter,we summarize the main research results and prospects of this paper.