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中心化L2偏差已被用来作为部分因析设计均匀性的度量,并用来区分几何非同构设计.中心化L2偏差均值也被用来度量部分因析设计均匀性,这样就可以对现有最小低阶混杂设计进行水平置换,从而获得中心化L2偏差最小的均匀最小低阶混杂设计.本文里,我们针对三水平部分因析设计讨论中心化L2偏差均值的性质,给出中心化L2偏差均值与正交性准则,最小低阶矩混杂准则之间的解析关系,同时给出中心化L2偏差均值的两个下界. 相似文献
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非黏滞阻尼模型相比传统黏滞阻尼模型能更准确描述结构材料的耗能行为,其本构关系常用核函数为指数函数的卷积形式表示.针对目前非黏滞阻尼结构的随机地震动响应分析方法所得结果较为复杂,该文提出了一种基于Clough-Penzien(C-P)谱的结构响应0~2阶谱矩分析的简明封闭解法.该方法首先提出非黏滞阻尼结构的精确等效微分本构关系式,并利用其与C-P谱滤波微分方程重构了结构的地震动方程;再基于随机振动理论获得了结构随机响应0~2阶谱矩的简明封闭解,并基于得到的0~2阶谱矩采用首次超越破坏准则和Markov分布规则进行了结构动力可靠度分析;最后通过算例论证了该简明封闭解的准确性及高效性. 相似文献
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YANG Guijun LIU Minqian & ZHANG Runchu Department of Statistics Tianjin University of Finance Economics Tianjin China Department of Statistics School of Mathematical Sciences LPMC Nankai University Tianjin China 《中国科学A辑(英文版)》2005,(11)
Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some 2IVm-p designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs. And some conditions are provided, under which a 2IVm-p design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time. Some weak minimum aberration 2IVm-p designs are provided for illustrations and two non-isomorphic weak minimum aberration 2IV13-6 designs are constructed at the end of this paper. 相似文献
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Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. In this paper, we study matrix image theory and present a new method for distinguishing and assessing nonregular designs with complex alias structure, which works for all symmetrical and asymmetrical, regular and nonregular orthogonal arrays. Based on the matrix image theory, our proposed method captures orthogonality and projection properties. Empirical studies show that the proposed method has a more precise differentiation capacity when comparing with some other criteria. 相似文献
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Hong Qin Ming-yao Ai Jian-hui Ning 《应用数学学报(英文版)》2005,21(4):545-552
A fundamental and practical question for fractional factorial designs is the issue of optimal factor assignment. Recently, some new criteria, such as generalized minimum aberration, WV-criterion, NB-criterion and uniformity criterion are proposed for comparing and selecting fractions. In this paper, we indicate that these criteria agree quite well for symmetrical fraction factorial designs. 相似文献
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Yuanzhen HeMingyao Ai 《Statistics & probability letters》2012,82(3):542-547
The complementary design theory is powerful for searching for an optimal design when its complementary design is smaller. This paper introduces a new class of sliced equidistance designs and develops the corresponding complementary design theory under the generalized minimum aberration criterion. Two rules are established to search for a generalized minimum aberration design through its complementary design in a sliced equidistance design. As a result, the developed theory covers the related results for the whole designs being saturated designs as special cases. Some examples are presented to illustrate its usefulness. 相似文献
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Minimum secondary aberration fractional factorial split-plot designs in terms of consulting designs 总被引:1,自引:0,他引:1
AI Mingyao & ZHANG Runchu Key Laboratory of Pure Applied Mathematics School of Mathematical Sciences Peking University Beijing China Key Laboratory of Pure Mathematics Combinatorics School of Mathematical Sciences Nankai University Tianjin China 《中国科学A辑(英文版)》2006,49(4):494-512
It is very powerful for constructing nearly saturated factorial designs to characterize fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary wordlength pattern of a regular symmetrical fractional factorial split-plot (FFSP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial design theory and coding theory, we obtain some general and unified combinatorial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to these identities, we further establish some general and unified rules for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs. 相似文献
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WEI JiaLin YANG JianFeng LI Peng & ZHANG RunChu School of Mathematical Sciences LPMC Nankai University Tianjin China KLAS School of Mathematics Statistics Northeast Normal University Changchun School of Mathematical Sciences Capital Normal University Beijing School of Sciences Tianjin University of Commerce Tianjin 《中国科学 数学(英文版)》2010,(4)
Split-plot designs have been widely used in industrial experiments.Up to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) criterion.Recently,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et al.proposed a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) theory.It is proved that,the GMC criterion selects optimal designs ... 相似文献
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Fractional factorial designs are popular and widely used for industrial experiments. Generalized minimum aberration is an important criterion recently proposed for both regular and non-regular designs. This paper provides a formal optimization treatment on optimal designs with generalized minimum aberration. New lower bounds and optimality results are developed for resolution-III designs. Based on these results, an effective computer search algorithm is provided for sub-design selection, and new optimal designs are reported. 相似文献
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Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some 2m-p Ⅳ designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs.And some conditions are provided, under which a 2m-p Ⅳ design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time.Some weak minimum aberration 2m-p Ⅳ designs are provided for illustrations and two nonisomorphic weak minimum aberration 213-6 Ⅳ designs are constructed at the end of this paper. 相似文献
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Anton Betten Reinhard Laue Sergey Molodtsov Alfred Wassermann 《Journal of Geometry》2000,67(1-2):35-41
The first 5-(72, 6, 1) designs with automorphism group PSL(2, 71) were found by Mills [10]. We presently enumerate all 5-(72, 6, 1) designs with this automorphism group. There are in all 926299 non-isomorphic designs. We show that a necessary condition for semiregular5-(v, 6, 1) designs with automorphism group PSL(2, v 1) to exist is thatv=84, 228 (mod 360). In particular, there are exactly 3 non-isomorphic semiregular 5-(84, 6, 1) designs with automorphism group PSL(2, 83). There are at least 6450 non-isomorphic 5-(244, 6, 1) designs with automorphism group PL(2, 35). 相似文献
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Many construction methods for (nearly) uniform designs have been proposed under the centered $L_2$ -discrepancy, and most of them are only suitable for constructing designs with small size. This paper proposes a new method, called mixture method (MM), to construct nearly symmetrical/asymmetrical uniform designs with large number of runs and/or large number of factors. The new method has the “better than given” property, i.e., the resulting design is better than existing designs in the sense of the pre-decided criterion. Moreover, the computational speed of MM is faster than most existing methods. 相似文献