【作者】 赵娜；

【导师】 张崇岐；

【作者基本信息】 广州大学 ， 应用数学， 2007， 硕士

【摘要】 混料试验在工农业生产、科学研究和经营管理中应用非常广泛.混料试验设计方法有很多种.在q分量正规单纯形利益区域S_q-1上,对于q分量二阶可加混料模型[16～20],作者利用对称的轴设计,矩阵代数理论,数值方法,D-最优设计理论,A-最优设计理论,给出了此模型参数估计的D-最优轴设计及A-最优轴设计.对于上述模型,参数估计的D-最优轴设计是:设ξA是一个具有2q个试验点的对称轴设计,由于设计中试验点的个数等于待估参数的个数,此设计是饱和的,每个试验点配置的测度相等,均为1/（2q）.当3≤q≤5和q≥7时,分别得到两组设计点,进一步证明了配置等测度1/（2q）到这些设计点的饱和轴设计是S_q-1上的D-最优饱和轴设计.由于A-最优性对每个分量的权重不是相同的,与上述模型参数估计的D-最优轴设计相比,A-最优轴设计要复杂很多,当3≤q≤6时,在由D-最优轴设计所确定的设计点的基础上,作者讨论并获得了可加混料模型的轴设计类上的A-最优轴设计.更多还原

【Abstract】 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 .更多还原