中文摘要：

离散偏差经常用来衡量部分因子设计的均匀性,偏差的准确下界可以检验给定设计的均匀程度.基于现有的离散偏差的公式,讨论了二、三混水平设计离散偏差的下界问题,并利用泰勒展开的方法给出一个新的下界.与已有的下界相比,所给出的下界在某些设计中更精确.

英文摘要：

The discrete discrepancy is often evaluated the uniformity of factorial designs. The accurate lower bounds of discrepancies can test uniform degree of designs. On the basis of existing formula of the discrete discrepancy,this article discusses lower bounds to discrete discrepancy in mixed two-and three- level fractional factorial designs and gives a new lower bound to the discrete discrepancy according to Taylor expansion. The new lower bound is better than existing lower bounds in certain factorials designs. Finally,two examples are given to illustrate the results.