混水平饱和正交设计在广义离散偏差下的均匀性

针对二、三混水平饱和正交设计d,在适当的划分下d=(D:),给出设计d的广义离散偏差与子设计D()的广义字长型及均匀性模式的解析关系.同时,给出这类因子设计的广义离散偏差的下界.最后,通过例子来验证其结论.

Uniformity in mixed levels saturated orthogonal designs in term of generalized discrete discrepancy

In this paper, we consider a kind of mixed two and three levels saturated orthogonal designs. Under a proper decomposition of $d=(Dvdots bar{D})$, we give connections between the generalized discrete discrepancy of $d$ and generalized word length pattern or uniformity pattern of $D$ or $(bar{D})$, meanwhile, we also present the lower bound of generalized discrete discrepancy of this kind of fractional factorials. Finally, an illustrative example is given to shown our theoretical results.