互补设计在广义离散偏差下的均匀性

Uniformity in complementary designs in term of generalized discrete discrepancy

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.

In this paper, we consider a special kind of designs d = （D D） with two and three mixed levels. Under a proper decomposition, the connections between uniformity measured by generalized discrete discrepancy and generalized word length pattern or uniformity pattern for a pair of complementary designs d are obtained, and a lower bound of generalized discrete discrepancy of this kind of fractional factorials is obtained. Finally, an illustrative example is given to shown our theoretical results.