Study On Robust D-, R-optimal Designs For Mixture Models

Mixture experiment is an optimum proportion research for q influencing fac-tors of a certain characteristic index of the product, and it has been widely used in agriculture, industry, pharmacy, traditional Chinese medicine, and so on. In the mixture experiment design, the optimal mix of mixtures is often obtained under certain concrete mixtures model and optimal criterion. However, it will lead to the change of the response variable, if the proportion of a component changes or the choices for mixture models are difference. Then robust design is designed to meet the conditions when the impact factor changes slightly and the response variable is insensitive to change. Thus, firstly in this paper, it uses optimal criterions of mod-el of robust D-optimal designs and their related theories to obtain model robust D-optimal design for four components second degree additive model which is one type of second degree additive models. In addition, it uses maximin principle of efficiency designs to obtain a priori measurement according to robust D-optimal design.Secondly, it studies mixture K model for q components second degree and obtain a R-optimal design under the models by using the R - optimal design criterion. Then, in the light of related theories of model robust R-optimal design,it obtains an optimal allocation of model robust R-optimal for the second degree mixture K model. Furthermore, it gets a prior measurement of model robust R-optimal designs for three components second degree mixture models by using maximin principle of efficiency designs.