二三混水平因子设计离散偏差新的下界

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.

互补设计在Lee偏差下的均匀性

针对两类特殊的二、三混水平部分因子设计d=(D■),在适当的划分下分别给出了互补设计的Lee偏差与子设计D()的广义字长型和均匀性模式的解析关系,同时给出了Lee偏差的下界,最后通过两个例子来验证其结论.

互补设计在广义离散偏差下的均匀性

针对一类特殊的二、三混水平部分因子设计d=(D■D),在适当的划分下分别给出了互补设计的广义离散偏差与子设计D(D)的广义字长型及均匀性模式的解析关系,同时给出了互补设计的广义离散偏差的下界,最后通过例子来验证其结论.

Some Results on Minimum Aberration Mixed-level (2~r)2~n Factorial Designs

Mukerjee and Wu（2001） employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4. In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level （2^r）2^n factorial design to that of its consulting design. Consequently, a general rule for identifying minimum aberration （2^r）2^n factorial designs through their consulting designs is established. It is an improvement and generalization of the related result in Mukerjee and Wu（2001）.