均匀设计作为一种空间填充设计，由于具有灵活的试验次数和模型稳健性被广泛运用到各个领域.倍扩方法在构造具有优良性质的二水平部分因析设计中起着非常重要的作用.本文将二水平设计的倍扩构造方法推广至四水平，二、四混水平设计，分别提出了四水平和二、四混水平倍扩设计的新概念，在可卷L2-偏差意义下研究了二水平，四水平，二、四混水平倍扩设计与其初始设计均匀性之间的关系.同时获得这些倍扩设计的可卷L2-偏差的新下界，这些下界为评价倍扩设计的均匀性提供一个基准.最后讨论了倍扩设计的均匀性.
Abstract
As a type of space-filling designs, uniform designs are widely applied in various fields because of flexibility of runs and model robustness. The method of doubling plays an important role in construction of optimal two-level designs. In this paper, the construction of doubling for two-level designs is extended to four-level and mixed two- and four-level designs, the new conception on four-level and mixed two- and four-level Double designs are presented. Under the wrap-around L2-discrepancy, the relationships of uniformity between such Double designs and their initial designs are investigated. Moreover, some new lower bounds of wrap-around L2-discrepancies for such Double designs are obtained, which can be used as a benchmark to evaluate the uniformity of Double designs. Finally, the uniformity of Double designs is discussed.
关键词
均匀设计 /
倍扩设计 /
可卷L2-偏差 /
下界 /
设计效率
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Key words
uniform design /
double design /
wrap-around L2-discrepancy /
lower bound /
design efficiency
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参考文献
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[17] 李洪毅. 博士学位论文:基于折叠反转与编码映射的最优部分因析设计构造方法研究. 武汉:华中师范大学, 2018(Li H Y. Ph. D Thesis:Study on Construction Method of Optimal Fractional Factorial Designs Via Foldover and Code Mapping. Wuhan:Central China Normal University, 2018)
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脚注
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基金
国家自科基金项目（11701213，11961027，11561025，11871237），湖南省自然科学基金项目（2017JJ2218，2017JJ3253），湖南省教育厅重点项目（18A284，19A403），湘西州科技创新项目（2018SF5022，2018SF5023），2018年度吉首大学引进人员科研资助项目.
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