对某些参数GMC设计试验安排的研究

发布时间：2017-12-31 14:29

  本文关键词：对某些参数GMC设计试验安排的研究　出处：《东北师范大学》2015年硕士论文　论文类型：学位论文

  更多相关文章： 部分因析设计 因子的别名效应模型 效应等级原则 因子效应 一般最小低阶混杂 最小低阶混杂 因子安排

【摘要】：试验设计作为统计学的重要分支,其理论和应用研究非常广泛。其中多因子试验(即因析试验)是试验设计的一个极为重要和基础的研究领域。为实现实际试验的最优化,有两类研究问题:一类是对各类实际试验如何寻找最优设计;另一类是有了设计之后如何最优地安排因子到设计的列实施试验以达到试验和分析的最优精度。对于前者已有大量理论成果和各类最优设计构造结果。而对于后者,近些年才出现一些系统的理论和应用研究成果。为此,首先对二水平正规因析设计类,Zhou,BalakrishnanZhang[1]提出了一个关于因子的别名效应个数模式,记为F-AENP,作为度量在设计中各列及其关联效应被混杂严重性程度的指标,并根据效应等级原则给出了列的优劣排序准则。同时对二水平正规设计类{2n-m:n,m为正整数,n-m0}中的最优设计GMC设计类,按照F-AENP给出了当5N/16+1≤nN/2和N/2≤n≤N-1时设计列的优劣排序,其中N=2n-m,为试验run的个数,n为因子个数。这些结果为试验者将依次重要的因子安排到设计的依次优劣的列上从而实现最优试验和分析提供了方便。根据ZhangCheng[2]给出的结论,在同构意义下,9N/32+1≤n5N/16,17N/64+1≤n9N/32和33N/128+1≤n17N/64三个区域内所有的GMC设计分别是SOS设计S(5N/16),S(9N/32)和S(17N/64)的投影并恰为变换Yates Oder(即RC-Yates Order)下饱和设计Hq的后n列。于是,计算n=N/2,n=5N/16,n=9N/32时GMC设计因子的F-AENP具有决定意义。本文完成了对n=N/2,n=5N/16,n=9N/32所有GMC设计的F-AENP的计算,并且给出了各列好坏程度的排序,这为给出上述三区域全部GMC设计的按F-AENP的优劣排序奠定了基础。文中结论后附有实例,便于试验者理解和应用。而后针对9N/32+1≤n5N/16时GMC设计F-AENP的计算给出理论计算公式,并对设计各列进行了非降序排列及附以简单实例,为以后的研究提供参考。
[Abstract]:Experimental design is an important branch of statistics. The theory and application of the experiment are very extensive, and the multi-factor test (i.e. the factor analysis test) is an extremely important and basic research field of the experimental design, in order to realize the optimization of the actual test. There are two kinds of research problems: one is how to find the optimal design for all kinds of practical experiments; The other is how to best arrange the factors to the design column to achieve the optimal precision of the test and analysis after the design. For the former, there are a lot of theoretical results and various kinds of optimal design construction results. Who. In recent years, some systematic theoretical and applied research results have emerged. For this reason, first of all, the two-level normal factorial analysis design class Zhou-Balakrishnan Zhang. [1] A model of aliasing effect number of factors is proposed, which is described as F-AENPs, as an index to measure the severity of confounding effects of each column and its correlation effects in the design. According to the principle of effect hierarchy, the ranking criterion of columns is given, and the optimal design GMC design class in the class {2n-m: nm is a positive integer n-m0} is also given for the two level normal design class {2n-m: nm. According to F-AENP, we give the sequence of the design columns when 5N / 161 鈮，

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