整区因子较重要时裂区设计的最优性理论
发布时间：2019-05-11 21:22
【摘要】：假设一个试验中有n个因子,每个因子有两个水平,其中有n1个因子的水平难以改变或改变花费较多,另外n2(= n -n1 个因子的水平比较容易改变.把水平难以改变的因子称作整区(Whole plot, WP)因子,水平容易改变的因子称作子区(sub-plot)因子.显然,这两类因子不再有相同的地位,这种情况常采用部分因子裂区(Fractional factorial split-plot)设计实施试验.在实施部分因子裂区试验时需要进行两阶段随机化,从而在方差分析模型中产生两个误差项,分别是整区误差项和子区误差项.很多试验的经验表明,整区误差大于子区误差.这意味着这两类因子在数据分析中的影响是不同的,整区因子比子区因子在试验中有更重要的地位.最小低价混杂(Minimum aberration, MA)准则是选取最优设计的常用准则之一.文献中关于裂区设计的MA准则假设整区因子和子区因子具有相同的地位.本文在整区因子比子区因子在试验中更重要这一假设下,首先建立了一个新的选择部分因子裂区设计的准则.即整区因子较重要时的最小低阶混杂(WP-MA)准则,然后研究了部分因子裂区设计在WP-MA准则下的性质,给出了在k1和k2较小时,部分因子裂区设计2(n1+n2)-(k1+k2)在WP-MA准则下的最优设计的构造方法.
[Abstract]:Suppose there are n factors in an experiment, each factor has two levels, in which the level of n 1 factor is difficult to change or cost more to change, and the level of n 2 (= n-n 1 factor) is easier to change. The factor whose level is difficult to change is called the whole region (Whole plot, WP) factor, and the factor whose level is easy to change is called sub-plot factor. Obviously, these two kinds of factors no longer have the same status, which often adopts partial factor split zone (Fractional factorial split-plot) to design and carry out the test. It is necessary to carry out two stages randomization in the implementation of partial factor split zone test, so as to produce two error terms in the ANOVA model, namely, the whole region error term and the subregion error term. Many experiments have shown that the whole region error is larger than the sub-zone error. This means that the influence of these two kinds of factors in data analysis is different, and the whole region factor plays a more important role in the experiment. The minimum low-cost hybrid (Minimum aberration, MA) criterion is one of the commonly used criteria for selecting optimal design. The MA criterion for crack zone design in the literature assumes that the whole region factor and the subgroup factor have the same position. In this paper, under the assumption that the whole region factor is more important than the region factor in the experiment, a new criterion for selecting the partial factor crack region design is established. That is, the minimum low order hybrid (WP-MA) criterion when the whole region factor is important, and then the properties of the partial factor crack region design under the WP-MA criterion are studied, and the properties of the partial factor crack region design under the WP-MA criterion are given. The construction method of optimal design of partial factor crack region design 2 (n1n2)-(k1k2) under WP-MA criterion.
【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：2474863
[Abstract]:Suppose there are n factors in an experiment, each factor has two levels, in which the level of n 1 factor is difficult to change or cost more to change, and the level of n 2 (= n-n 1 factor) is easier to change. The factor whose level is difficult to change is called the whole region (Whole plot, WP) factor, and the factor whose level is easy to change is called sub-plot factor. Obviously, these two kinds of factors no longer have the same status, which often adopts partial factor split zone (Fractional factorial split-plot) to design and carry out the test. It is necessary to carry out two stages randomization in the implementation of partial factor split zone test, so as to produce two error terms in the ANOVA model, namely, the whole region error term and the subregion error term. Many experiments have shown that the whole region error is larger than the sub-zone error. This means that the influence of these two kinds of factors in data analysis is different, and the whole region factor plays a more important role in the experiment. The minimum low-cost hybrid (Minimum aberration, MA) criterion is one of the commonly used criteria for selecting optimal design. The MA criterion for crack zone design in the literature assumes that the whole region factor and the subgroup factor have the same position. In this paper, under the assumption that the whole region factor is more important than the region factor in the experiment, a new criterion for selecting the partial factor crack region design is established. That is, the minimum low order hybrid (WP-MA) criterion when the whole region factor is important, and then the properties of the partial factor crack region design under the WP-MA criterion are studied, and the properties of the partial factor crack region design under the WP-MA criterion are given. The construction method of optimal design of partial factor crack region design 2 (n1n2)-(k1k2) under WP-MA criterion.
【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
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