混水平列扩充设计的均匀性

在许多工业应用中,通常分步应用跟随设计来考察输入(因子)和产出(响应)间的关系.在许多跟随设计中,在跟随阶段可以加入一些另外的两水平或三水平因子,因为它们在初始阶段可能被忽略但又十分重要.文章在均匀性准则下,提出了中心化L2-偏差意义下的混水平列扩充均匀设计,给出了列扩充设计在中心化L2-偏差下的解析表达式及相应的下界,其可作为搜索均匀设计的基准.进一步,具有一个附加区组因子的列扩充设计是均匀的当且仅当未加区组因子时的列扩充设计是均匀的.

Uniformity of Mixed-Level Column Augmented Designs

In many industrial applications,follow-up experimental designs are often used to explore the relationship between inputs(factors)and outputs(responses)step by step.In many follow-up designs,some extra factors with two or three levels may be added in the follow-up stage since they are quite important but may be neglected in the initial stage.In this paper,mixed-level column augmented uniform designs are proposed under the centered L2-discrepancy.The analytical expressions and the corresponding lower bounds on centered L2-discrepancy of the mixed-level column augmented designs are presented,which can be used as a benchmark for searching uniform design.Furthermore,the column augmented design with one additional block factor is uniform if and only if the column augmented design is uniform when no block factor is added.