MEC准则下的正规对称部分因子设计
发布时间：2018-11-26 13:30
【摘要】：因子设计已经被广泛运用到各个试验研究领域.在因子个数比较多,但是试验又受时间、经费等因素的限制不能对所有的因子水平组合实施试验时,常采用部分因子试验.分区组是试验设计的基本原则之一.当试验单元不能满足齐性时,常采用分区组设计.构造各类最优设计是试验设计领域的重要研究内容.本文主要研究正规对称部分因子设计的一个模型稳健性准则—估计容量准则.最大估计容量(maximum estimation capacity,简记为MEC)是在3阶及3阶以上交互作用可忽略的条件下选择一个设计使其能够估计尽可能多的包含所有主效应和部分两因子交互作用的模型.由于MEC准则要求太强,本文提出了弱化的MEC准则(Partial maximum estimation capacity,简记为 PMEC).探讨了最小低阶混杂(Minimum aberration,简记为MA)准则与MEC和PMEC准则的关系,证明了当k = 1时,MA 2n-k设计就是MEC设计,当k = 2,3时,MA 2n-kk设计就是PMEC设计.给出了 kk比较小时,在MEC准则或PMEC准则下二水平部分因子设计2n-k的最优设计的构造方法.本文还研究了在MEC或PMEC准则下全因子最优区组设计的构造方法,证明了 MEC 2n : 2s设计与MA 2n : 2s设计是相同的,给出了k,s都较小时,分区组部分因子设计2n-k-:2s的最优设计的构造方法.
[Abstract]:Factor design has been widely used in various experimental research fields. When the number of factors is quite large, but the test is limited by time and cost, and so on, some factor tests are often used when all factors can not be combined with each other. Partition group is one of the basic principles of experimental design. When the test unit can not satisfy the homogeneity, the partition group design is often used. Constructing various kinds of optimal design is an important research content in the field of experimental design. In this paper, a model robustness criterion for normal symmetric partial factor design, the capacity estimation criterion, is studied. The maximum estimated capacity (maximum estimation capacity,) is abbreviated to MEC). Under the condition that the interaction of order 3 and above is negligible, a design is chosen to estimate as many models as possible which include all the main effects and some of the two factors interaction. Because of the strong requirement of MEC criterion, this paper proposes a weak MEC criterion (Partial maximum estimation capacity, is abbreviated to PMEC). This paper discusses the relation between the minimum low order hybrid (Minimum aberration, (MA) criterion and the MEC and PMEC criteria. It is proved that when k = 1, MA 2n-k design is MEC design, and when k = 2,3, MA 2n-kk design is PMEC design. The construction method of optimal design of two-level partial factor design 2n-k under MEC criterion or PMEC criterion is given. In this paper, we also study the construction method of the whole factor optimal block design under the MEC or PMEC criterion. It is proved that the MEC 2n: 2s design is the same as the MA 2n: 2s design, and it is shown that the MEC 2n: 2s design is smaller than that of the MA 2n: 2s design. The construction method of optimal design for partitioned group partial factor design (2n-k-:2s).
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C81
本文编号：2358696
[Abstract]:Factor design has been widely used in various experimental research fields. When the number of factors is quite large, but the test is limited by time and cost, and so on, some factor tests are often used when all factors can not be combined with each other. Partition group is one of the basic principles of experimental design. When the test unit can not satisfy the homogeneity, the partition group design is often used. Constructing various kinds of optimal design is an important research content in the field of experimental design. In this paper, a model robustness criterion for normal symmetric partial factor design, the capacity estimation criterion, is studied. The maximum estimated capacity (maximum estimation capacity,) is abbreviated to MEC). Under the condition that the interaction of order 3 and above is negligible, a design is chosen to estimate as many models as possible which include all the main effects and some of the two factors interaction. Because of the strong requirement of MEC criterion, this paper proposes a weak MEC criterion (Partial maximum estimation capacity, is abbreviated to PMEC). This paper discusses the relation between the minimum low order hybrid (Minimum aberration, (MA) criterion and the MEC and PMEC criteria. It is proved that when k = 1, MA 2n-k design is MEC design, and when k = 2,3, MA 2n-kk design is PMEC design. The construction method of optimal design of two-level partial factor design 2n-k under MEC criterion or PMEC criterion is given. In this paper, we also study the construction method of the whole factor optimal block design under the MEC or PMEC criterion. It is proved that the MEC 2n: 2s design is the same as the MA 2n: 2s design, and it is shown that the MEC 2n: 2s design is smaller than that of the MA 2n: 2s design. The construction method of optimal design for partitioned group partial factor design (2n-k-:2s).
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C81
【相似文献】
相关期刊论文 前1条
1 陈慧媛;;浅议企业实力评价综合因子设计[J];职业技术;2007年06期
相关硕士学位论文 前4条
1 仲亚苹;MEC准则下的正规对称部分因子设计[D];曲阜师范大学;2017年
2 朱玉杰;定量因子设计的字次型[D];苏州大学;2015年
3 邹娜;因子设计中几种重要准则之间的关系研究[D];华中师范大学;2007年
4 王晓丽;因子设计的重量计数器及其两种字长型的关系[D];苏州大学;2013年
，本文编号：2358696
本文链接：https://www.wllwen.com/shekelunwen/shgj/2358696.html
