基于tripling的补设计的性质研究

Study on properties of complementary designs via tripling

针对构成三水平等距设计D的一组互补设计d,d^(-)和tripling得到的Triple设计T(d),d^(-),讨论了子设计d^(-)和其补设计d的Triple设计T(d)之间的关系,建立了子设计d的Triple设计T(d)的可卷型L-偏差与其补设计d^(-)的字长型模式之间的关系,并且给出了设计T(d)与d^(-)之间的字长型模式的解析关系,最后基于可卷型L-偏差讨论了设计T (d)与d^(-)之间的均匀性关系并获得了相应的下界.这些关系为利用较少因子、较少试验研究较多因子、较多试验设计的性质提供了理论基础.

For the complementary designs d,d^(-) composed of a three-level equidistant designs D and their Triple designs T(d),d^(-) by tripling,the relationship between the subdesign d^(-) and the Triple design of its complementary design T(d) is considered,the relationship between the wrap-around L-discrepancy of the Triple design of d denoted by T(d) and the generalized wordlength pattern of the complementary design of d denoted by d^(-) is built.Moreover the analytical connection of the generalized wordlength pattern between T(d) and d^(-) is presented. The relationship of uniformity between d^(-) and T(d) is discussed,and the lower bounds of such designs are obtained based on the wrap-around L-discrepancy. These results obtained provide theoretical basis for studying the properties of the design with more factors,more runs by the design with fewer factors,fewer runs.