V-optimal Designs For Mixture Experiment Model With Random Varying-coefficients

Random varying-coefficient model is a new development model in recent years, it has a wide range of applications in agriculture, medicine and biology, and so on. Most of research works are focused on statistical inferences and analyses of postulated models. Optimal designs under random varying-coefficient models haven't fully developed.This thesis mainly discuss V-optimal designs under several kinds of classical models. Through example, we prove V-design superiority of model. We change the random varying-coefficient model into the mix effect model. In the process of solving the maximum value, we use lagrangian multiplier method to get extreme values.The construction of this thesis is assembled by 5 parts.In chapter 1, we introduce random varying-coefficient models and then show objectiveness and significance of our work together with literature review.In chapter 2, we introduce the designs of mixture experiments. Some classical models and V-optimal criterion are discussed in this chapter too.In chapter 3, we show the process of changing random varying-coefficient mod-els to mixed-effects linear models.In chapter 4, V-optimal designs for Scheffe random coefficient model are dis-cussed. Also we show designs for Becker random varying-coefficient models and random varying-coefficient K-models. The description of example about insecticide can show optimum of V-optimal designs.Finally, we give a summarize of our works in the last section. A review of works that may be done in the future is given in this section too.