多个区组变量的最优设计理论
发布时间：2018-11-05 16:35
【摘要】：因子设计在试验中有广泛运用,随机化是试验设计的基本原则之一.对试验进行随机化的前提条件是各试验单元具有齐性.由于实际条件等难以控制因素的限制,各试验单元的齐性难以保证,这会导致试验结果的精度下降.这时,试验者往往采取区组设计实施试验.由于分区组设计在我们生活中有广泛的应用,对它的研究一直是试验设计研究领域的一个热门课题.目前,国际上对于分区组设计的研究基本上都是单区组变量的分区组设计.最小低阶混杂(minimum aberration,MA)准则是选择最优设计的常用准则.由于目前国际上对于在MA准则下关于多个区组变量情形下最优分区组设计的研究几乎是空白,本文主要研究在MA准则下具有多个区组变量的最优区组设计理论.首先提出了多个区组变量的分区组设计的效应分层原则,在该原则下定义了相应的字长型,然后提出了多个区组变量分区组设计的最小低阶混杂(multiple blocked minimum aberration, MBMA)准则.本文主要研究了在MBMA准则下具有两个区组变量和三个区组变量的全设计的最优分区组设计的构造方法,从理论上构造出了这两类设计的MBMA设计.
[Abstract]:Factor design is widely used in experiments, randomization is one of the basic principles of experimental design. The premise of randomization is the homogeneity of each test unit. The homogeneity of each test unit is difficult to guarantee due to the limitation of difficult control factors such as actual conditions, which will lead to the decrease of the accuracy of the test results. At this point, the experimenter often takes the block design to carry out the experiment. Because of its wide application in our life, the study of partition group design has been a hot topic in the field of experimental design. At present, the international research on partition group design is basically single block variable partition group design. Minimum low order hybrid (minimum aberration,MA) criterion is commonly used to select optimal design. Since there is almost no research on the design of optimal partition groups in the case of multiple block variables under the MA criterion, this paper mainly studies the optimal block design theory with multiple block variables under the MA criterion. Firstly, the effect stratification principle of partition group design for multiple block variables is proposed, and the corresponding word length type is defined under this principle, and then the minimum low order hybrid (multiple blocked minimum aberration, MBMA) criterion for the partition group design of multiple block variables is proposed. In this paper, the construction method of optimal partition group design with two block variables and three block variables under MBMA criterion is studied, and the MBMA design of these two designs is constructed theoretically.
【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：2312659
[Abstract]:Factor design is widely used in experiments, randomization is one of the basic principles of experimental design. The premise of randomization is the homogeneity of each test unit. The homogeneity of each test unit is difficult to guarantee due to the limitation of difficult control factors such as actual conditions, which will lead to the decrease of the accuracy of the test results. At this point, the experimenter often takes the block design to carry out the experiment. Because of its wide application in our life, the study of partition group design has been a hot topic in the field of experimental design. At present, the international research on partition group design is basically single block variable partition group design. Minimum low order hybrid (minimum aberration,MA) criterion is commonly used to select optimal design. Since there is almost no research on the design of optimal partition groups in the case of multiple block variables under the MA criterion, this paper mainly studies the optimal block design theory with multiple block variables under the MA criterion. Firstly, the effect stratification principle of partition group design for multiple block variables is proposed, and the corresponding word length type is defined under this principle, and then the minimum low order hybrid (multiple blocked minimum aberration, MBMA) criterion for the partition group design of multiple block variables is proposed. In this paper, the construction method of optimal partition group design with two block variables and three block variables under MBMA criterion is studied, and the MBMA design of these two designs is constructed theoretically.
【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
【参考文献】
相关期刊论文 前1条
1 赵胜利;;正规部分因子设计的最优性理论与构造方法[J];应用概率统计;2015年03期
，本文编号：2312659
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