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首页> 外文期刊>Journal of applied statistics >A catalog of optimal foldover plans for constructing U-uniform minimum aberration four-level combined designs
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A catalog of optimal foldover plans for constructing U-uniform minimum aberration four-level combined designs

机译：构造U均匀最小像差四级组合设计的最佳折叠方案目录

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摘要

The foldover plan is a transformation map for adding a foldover design to the initial design, thus resulting in a combined design which can be used for breaking the links between aliased effects. This paper discusses the optimality of foldover plans for four-level designs via the most common criteria: the generalized word-length pattern (GWLP), Lee discrepancy (LD), wrap-around discrepancy (WD), centered discrepancy (CD) and mixture discrepancy (MD). We prove that the LD, WD and GWLP are equivalent for: any initial design and the corresponding foldover designs; any foldover design and its complementary foldover design; and any combined design and its complementary combined design. However, these interesting properties do not necessarily take place in the cases of the CD and MD. New analytical expressions and lower bounds of these discrepancies are given for initial and combined designs, which can be used as benchmarks for constructing uniform designs. For illustration of the usage of our theoretical results, a catalog of optimal foldover plans for constructing U-uniform minimum aberration four-level combined designs that involve factors with run is tabulated, which can be used for investigating either qualitative or quantitative factors.
机译：折叠计划是一个转换图，用于将折叠设计添加到初始设计中，从而产生可用于打破混叠效果之间联系的组合设计。本文通过最普遍的标准讨论四级设计的折叠方案的最优性：广义字长模式（GWLP），Lee差异（LD），环绕式差异（WD），居中差异（CD）和混合差异（MD）。我们证明LD，WD和GWLP在以下方面是等效的：任何初始设计和相应的折叠设计；任何折叠设计及其互补的折叠设计；以及任何组合设计及其互补的组合设计。但是，在CD和MD的情况下，这些有趣的属性不一定会发生。针对初始设计和组合设计给出了新的分析表达式和这些差异的下限，可以用作构建统一设计的基准。为了说明我们的理论结果的用法，列出了用于构造涉及运行因子的U均匀最小像差四级组合设计的最佳折叠计划的目录，可用于研究定性或定量因素。

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