Optimal Axial Designs For Mixture Experiments

Mixture experiments have extremely wide application in industrial and agricul-tural production,scientific research , operation and management. There are manymethods to design mixture experiments. In q-components standard simplex inter-est region Sq-1 , we obtain D-optimal axial designs and A-optimal axial designs ofparameters'estimation for the quadratic additive mixture model[16～20] using matrixalgebra theory , numerical , D-optimality theory and A-optimality theory. LetξA bea symmetric axial design with 2q support points. The numbers of its support pointsare equal to that of the estimating parameters. The design is saturated and the mea-sures of each support points are equal to 1/(2q) . For 3≤q≤5 and q≥7 , twogroups support points are obtained. Further, it is proved that the saturated axial designwith equal measure 1/(2q) is D-optimal saturated axial designs on region Sq-1 . ForA-optimality , the measure to each component is not equal. Compared to D-optimalaxial designs of parameters'estimation for this model , A-optimal axial designs ismore complicated. For 3≤q≤6 ,based on the support points determined by D-optimal axial designs , A-optimal axial designs are obtained .