三水平部分因析设计的中心化L_2偏差均值的几个结果

Some Results on Average Centered L_2-discrepancy of Three-Level Fractional Factorial Designs

中心化L_2偏差已被用来作为部分因析设计均匀性的度量,并用来区分几何非同构设计.中心化L_2偏差均值也被用来度量部分因析设计均匀性,这样就可以对现有最小低阶混杂设计进行水平置换,从而获得中心化L_2偏差最小的均匀最小低阶混杂设计.本文里,我们针对三水平部分因析设计讨论中心化L_2偏差均值的性质,给出中心化L_2偏差均值与正交性准则,最小低阶矩混杂准则之间的解析关系,同时给出中心化L_2偏差均值的两个下界.

The centered L2-discrepancy has been employed as the measure of uniformity and used to distinguish geometrically nonisomorphic designs. The average centered L2- discrepancy has also been applied to measure the uniformity of fractional factorial designs, so we can obtain uniform minimum aberration designs with the minimum centered L2- discrepancy by permuting levels of existing minimum aberration designs. In this paper, for the three-level fractional factorial designs, we discuss the properties of the average cen- tered L2-discrepancy, build the relationships among the average centered L2-discrepancy, the orthogonality criterion and MMA criterion, and obtain two different lower bounds on the average centered L2-discrepancy.