MEC準(zhǔn)則下的正規(guī)對(duì)稱部分因子設(shè)計(jì)
發(fā)布時(shí)間：2018-11-26 13:30
【摘要】：因子設(shè)計(jì)已經(jīng)被廣泛運(yùn)用到各個(gè)試驗(yàn)研究領(lǐng)域.在因子個(gè)數(shù)比較多,但是試驗(yàn)又受時(shí)間、經(jīng)費(fèi)等因素的限制不能對(duì)所有的因子水平組合實(shí)施試驗(yàn)時(shí),常采用部分因子試驗(yàn).分區(qū)組是試驗(yàn)設(shè)計(jì)的基本原則之一.當(dāng)試驗(yàn)單元不能滿足齊性時(shí),常采用分區(qū)組設(shè)計(jì).構(gòu)造各類最優(yōu)設(shè)計(jì)是試驗(yàn)設(shè)計(jì)領(lǐng)域的重要研究?jī)?nèi)容.本文主要研究正規(guī)對(duì)稱部分因子設(shè)計(jì)的一個(gè)模型穩(wěn)健性準(zhǔn)則—估計(jì)容量準(zhǔn)則.最大估計(jì)容量(maximum estimation capacity,簡(jiǎn)記為MEC)是在3階及3階以上交互作用可忽略的條件下選擇一個(gè)設(shè)計(jì)使其能夠估計(jì)盡可能多的包含所有主效應(yīng)和部分兩因子交互作用的模型.由于MEC準(zhǔn)則要求太強(qiáng),本文提出了弱化的MEC準(zhǔn)則(Partial maximum estimation capacity,簡(jiǎn)記為 PMEC).探討了最小低階混雜(Minimum aberration,簡(jiǎn)記為MA)準(zhǔn)則與MEC和PMEC準(zhǔn)則的關(guān)系,證明了當(dāng)k = 1時(shí),MA 2n-k設(shè)計(jì)就是MEC設(shè)計(jì),當(dāng)k = 2,3時(shí),MA 2n-kk設(shè)計(jì)就是PMEC設(shè)計(jì).給出了 kk比較小時(shí),在MEC準(zhǔn)則或PMEC準(zhǔn)則下二水平部分因子設(shè)計(jì)2n-k的最優(yōu)設(shè)計(jì)的構(gòu)造方法.本文還研究了在MEC或PMEC準(zhǔn)則下全因子最優(yōu)區(qū)組設(shè)計(jì)的構(gòu)造方法,證明了 MEC 2n : 2s設(shè)計(jì)與MA 2n : 2s設(shè)計(jì)是相同的,給出了k,s都較小時(shí),分區(qū)組部分因子設(shè)計(jì)2n-k-:2s的最優(yōu)設(shè)計(jì)的構(gòu)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).
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：C81
本文編號(hào)：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).
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：C81
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