本文關(guān)鍵詞：對(duì)某些參數(shù)GMC設(shè)計(jì)試驗(yàn)安排的研究　出處：《東北師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 部分因析設(shè)計(jì) 因子的別名效應(yīng)模型 效應(yīng)等級(jí)原則 因子效應(yīng) 一般最小低階混雜 最小低階混雜 因子安排

【摘要】：試驗(yàn)設(shè)計(jì)作為統(tǒng)計(jì)學(xué)的重要分支,其理論和應(yīng)用研究非常廣泛。其中多因子試驗(yàn)(即因析試驗(yàn))是試驗(yàn)設(shè)計(jì)的一個(gè)極為重要和基礎(chǔ)的研究領(lǐng)域。為實(shí)現(xiàn)實(shí)際試驗(yàn)的最優(yōu)化,有兩類研究問(wèn)題:一類是對(duì)各類實(shí)際試驗(yàn)如何尋找最優(yōu)設(shè)計(jì);另一類是有了設(shè)計(jì)之后如何最優(yōu)地安排因子到設(shè)計(jì)的列實(shí)施試驗(yàn)以達(dá)到試驗(yàn)和分析的最優(yōu)精度。對(duì)于前者已有大量理論成果和各類最優(yōu)設(shè)計(jì)構(gòu)造結(jié)果。而對(duì)于后者,近些年才出現(xiàn)一些系統(tǒng)的理論和應(yīng)用研究成果。為此,首先對(duì)二水平正規(guī)因析設(shè)計(jì)類,Zhou,BalakrishnanZhang[1]提出了一個(gè)關(guān)于因子的別名效應(yīng)個(gè)數(shù)模式,記為F-AENP,作為度量在設(shè)計(jì)中各列及其關(guān)聯(lián)效應(yīng)被混雜嚴(yán)重性程度的指標(biāo),并根據(jù)效應(yīng)等級(jí)原則給出了列的優(yōu)劣排序準(zhǔn)則。同時(shí)對(duì)二水平正規(guī)設(shè)計(jì)類{2n-m:n,m為正整數(shù),n-m0}中的最優(yōu)設(shè)計(jì)GMC設(shè)計(jì)類,按照F-AENP給出了當(dāng)5N/16+1≤nN/2和N/2≤n≤N-1時(shí)設(shè)計(jì)列的優(yōu)劣排序,其中N=2n-m,為試驗(yàn)run的個(gè)數(shù),n為因子個(gè)數(shù)。這些結(jié)果為試驗(yàn)者將依次重要的因子安排到設(shè)計(jì)的依次優(yōu)劣的列上從而實(shí)現(xiàn)最優(yōu)試驗(yàn)和分析提供了方便。根據(jù)ZhangCheng[2]給出的結(jié)論,在同構(gòu)意義下,9N/32+1≤n5N/16,17N/64+1≤n9N/32和33N/128+1≤n17N/64三個(gè)區(qū)域內(nèi)所有的GMC設(shè)計(jì)分別是SOS設(shè)計(jì)S(5N/16),S(9N/32)和S(17N/64)的投影并恰為變換Yates Oder(即RC-Yates Order)下飽和設(shè)計(jì)Hq的后n列。于是,計(jì)算n=N/2,n=5N/16,n=9N/32時(shí)GMC設(shè)計(jì)因子的F-AENP具有決定意義。本文完成了對(duì)n=N/2,n=5N/16,n=9N/32所有GMC設(shè)計(jì)的F-AENP的計(jì)算,并且給出了各列好壞程度的排序,這為給出上述三區(qū)域全部GMC設(shè)計(jì)的按F-AENP的優(yōu)劣排序奠定了基礎(chǔ)。文中結(jié)論后附有實(shí)例,便于試驗(yàn)者理解和應(yīng)用。而后針對(duì)9N/32+1≤n5N/16時(shí)GMC設(shè)計(jì)F-AENP的計(jì)算給出理論計(jì)算公式,并對(duì)設(shè)計(jì)各列進(jìn)行了非降序排列及附以簡(jiǎn)單實(shí)例,為以后的研究提供參考。
[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，

本文編號(hào)：1360174