【摘要】：假設(shè)一個(gè)試驗(yàn)中有n個(gè)因子,每個(gè)因子有兩個(gè)水平,其中有n1個(gè)因子的水平難以改變或改變花費(fèi)較多,另外n2(= n -n1 個(gè)因子的水平比較容易改變.把水平難以改變的因子稱作整區(qū)(Whole plot, WP)因子,水平容易改變的因子稱作子區(qū)(sub-plot)因子.顯然,這兩類因子不再有相同的地位,這種情況常采用部分因子裂區(qū)(Fractional factorial split-plot)設(shè)計(jì)實(shí)施試驗(yàn).在實(shí)施部分因子裂區(qū)試驗(yàn)時(shí)需要進(jìn)行兩階段隨機(jī)化,從而在方差分析模型中產(chǎn)生兩個(gè)誤差項(xiàng),分別是整區(qū)誤差項(xiàng)和子區(qū)誤差項(xiàng).很多試驗(yàn)的經(jīng)驗(yàn)表明,整區(qū)誤差大于子區(qū)誤差.這意味著這兩類因子在數(shù)據(jù)分析中的影響是不同的,整區(qū)因子比子區(qū)因子在試驗(yàn)中有更重要的地位.最小低價(jià)混雜(Minimum aberration, MA)準(zhǔn)則是選取最優(yōu)設(shè)計(jì)的常用準(zhǔn)則之一.文獻(xiàn)中關(guān)于裂區(qū)設(shè)計(jì)的MA準(zhǔn)則假設(shè)整區(qū)因子和子區(qū)因子具有相同的地位.本文在整區(qū)因子比子區(qū)因子在試驗(yàn)中更重要這一假設(shè)下,首先建立了一個(gè)新的選擇部分因子裂區(qū)設(shè)計(jì)的準(zhǔn)則.即整區(qū)因子較重要時(shí)的最小低階混雜(WP-MA)準(zhǔn)則,然后研究了部分因子裂區(qū)設(shè)計(jì)在WP-MA準(zhǔn)則下的性質(zhì),給出了在k1和k2較小時(shí),部分因子裂區(qū)設(shè)計(jì)2(n1+n2)-(k1+k2)在WP-MA準(zhǔn)則下的最優(yōu)設(shè)計(jì)的構(gòu)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.
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：C81

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本文編號：2474863