李智, 李智明. 正规部分因析设计别名成分数型的一些性质[J]. 应用概率统计, 2021, 37(6): 585-597. DOI: 10.3969/j.issn.1001-4268.2021.06.003
引用本文: 李智, 李智明. 正规部分因析设计别名成分数型的一些性质[J]. 应用概率统计, 2021, 37(6): 585-597. DOI: 10.3969/j.issn.1001-4268.2021.06.003
LI Zhi, LI Zhiming. Some Porperties of Aliased Component-Number Pattern for Regular Fractional Factorial Designs[J]. Chinese Journal of Applied Probability and Statistics, 2021, 37(6): 585-597. DOI: 10.3969/j.issn.1001-4268.2021.06.003
Citation: LI Zhi, LI Zhiming. Some Porperties of Aliased Component-Number Pattern for Regular Fractional Factorial Designs[J]. Chinese Journal of Applied Probability and Statistics, 2021, 37(6): 585-597. DOI: 10.3969/j.issn.1001-4268.2021.06.003

正规部分因析设计别名成分数型的一些性质

Some Porperties of Aliased Component-Number Pattern for Regular Fractional Factorial Designs

  • 摘要: 一般最小低阶混杂准则和最小混杂准则是挑选s\,(s\geq 2)水平最优正规部分因析设计的两个重要准则,其分类模式分别为别名成分数型与字长型.本文主要研究s水平正规设计的别名成分数型的一些性质,得到了s水平下字长型中的元素可以表示为别名成分数型的函数形式,揭示了别名成分数型与字长型之间的关系. 另一方面, 通过字长型也可以计算某些别名成分数型. 进一步,得到了二水平设计的一些别名成分数型之间的表达公式.

     

    Abstract: General minimum lower-order confounding and minimum aberration are two important criteria to select s\,(s\geq 2)-level optimal regular fractional factorial designs. Their classification are based on the aliased component-number and word-length patterns, respectively. The paper mainly studies some properties of the aliased component-number pattern for s-level regular designs. We obtain that the elements of word-length pattern are expressed as some functions of aliased component-numbers under s-level case. It reveals the relationship between the aliased component-number and word-length patterns. On the other hand, we can calculate some aliased component-numbers by word-length pattern. Further, the formulas of some aliased component-numbers are provided for two-level designs.

     

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