Generalized A-Optimal Axial Designs For Additive Mixture Model

Mixture experiments are widely used in the industry, agriculture, scientific re-search and business management. Experiment with mixture is a special type of ex-periment in which the response to a mixture of q components is assumed to dependonly on the proportions (?) but not on the total amount of the mixture. Theexperimental region is the (q ?1)-simplex (?). Due to this restriction, the usual polynomial models are not directly ap-plicable to mixture problem. Researchers proposed many mixture models and designswith mixture experiments. Scheffe′(1958, 1963) suggested the simplex lattice designand simplex centroid design respectively. These designs belong to boundary designs,that is, all support points are on the vertex, edges and barycentres of simplex. In orderto obtain more inner support points of simplex in designs, Cornell (1975) proposedaxial design. He applied Cox's method to mixture experiments. Axial design's sup-port points are on the axes for vertex and barycentres of simplex. Axial design is aefficient method in mixture data analysis. Along to ith axial of simplex Sq-1, otherj (j = i) mixture components have same rate. In mixture experiments, especiallychemical industry, there are many components to be selected by researcher. We canselect mixture components and obtain important variables using axial design. For anadditive quadratic mixture model on Sq-1, we obtain A-optimal axial design with qcomponents using matrix algebra theory, numerical methods, and so on.This thesis is divided into three chapters. The first chapter introduces the mix-ture problem and the usual methods of mixture designs. The second chapter de-scribes A-optimal designs for five and six components additive quadratic mixturemodel.Last,using computer-aid method, we obtain the A-optimal designs for additivequadratic mixture model with q components in the Chapter three.