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部分因析裂区(FFSP)设计因其特殊结构而具有重要的研究价值.一个FFSP设计中有两类因子: 全区(WP)因子和子区(SP)因子,它们可以组成3种两因子交互效应: WP两因子交互效应, WS两因子效应和SP两因子交互效应.本文在纯净效应准则下考虑分辨度III和IV的FFSP设计, 得到了FFSP设计中纯净WP两因子交互效应及WS两因子交互效应的最大数目的上、下界,给出了该数目达到下界的FFSP设计的构造方法,并进一步考察了这些构造方法的实际效果. 相似文献
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本文介绍了在效应稀疏性的前提下venter和Steel提出的分析无重复析因试验数据的方法,并将它们和下降Lenth方法,下降Dong方法一起作了较全面的模拟比较。 相似文献
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最近,Q准则被用来研究设计在模型未知前提下的投影效率,并用它作为因子筛选准则来筛选最优的设计.本文里,我们将讨论double设计D(d)与其初始设计d的Q准则之间的联系. 相似文献
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本文给出了构造包含最多纯净两因子交互效应2m-(m-k)Ⅲ设计的一种方法.对于某些设计参数m和k,验证了所构造的设计包含纯净两因子交互效应的数量多于Tang et al.(2002)所构造的设计.并且所构造的设计都给出了格子点表示. 相似文献
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混水平部分因析设计在各类试验中有广泛应用.纯净效应准则是用于选取最优部分因析设计的重要准则之一.本文考虑含有一个八水平因子、一个四水平因子和若干二水平因子的8×4×2~n混水平设计,给出了分辨度为Ⅲ和Ⅳ的该类混水平设计包含纯净两因子交互作用成分最大数的上界和下界.下界通过构造特定设计而得到. 相似文献
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杨贵军 《数学物理学报(A辑)》2006,26(6):963-967
该文给出了2IVm-p设计包含最多纯净两因子交互效应与该设计具有弱最小低阶混杂等价的几个条件.并在文章的末尾给出了一组既具有弱最小低阶混杂又包含最多纯净两因子交互效应的2IVm-p设计. 相似文献
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一种构造三水平因子超饱和设计的准则和算法 总被引:3,自引:0,他引:3
在工业统计试验和其他科学试验中,常遇到因子个数多而所允许的试验次数少的情况,这时要用到超饱和设计,以前的文章仅研究了二水平因子的超饱和设计,本文对于三水平因子的超饱和设计提出了一种基于典则相关意义下的优良性准则和构造算法,并给出了试验次数为9和18可分别安排到26和30个因子的三水平超饱和设计表。 相似文献
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ZI Xuemin ZHANG Runchu & LIU Minqian Department of Statistics School of Mathematical Sciences LPMC Nankai University Tianjin China 《中国科学A辑(英文版)》2006,49(12)
Fractional factorial split-plot (FFSP) designs have an important value of investigation for their special structures. There are two types of factors in an FFSP design: the whole-plot (WP) factors and sub-plot (SP) factors, which can form three types of two-factor interactions: WP2fi, WS2fi and SP2fi. This paper considers FFSP designs with resolutionⅢorⅣunder the clear effects criterion. It derives the upper and lower bounds on the maximum numbers of clear WP2fis and WS2fis for FFSP designs, and gives some methods for constructing the desired FFSP designs. It further examines the performance of the construction methods. 相似文献
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《中国科学A辑(英文版)》2008,(7)
Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs,and it has become an active research issue in recent years.Tang et al.derived upper and lower bounds on the maximum number of clear two-factor interactions(2fi's) in 2n-(n-k) fractional factorial designs of resolutions III and IV by constructing a 2n-(n-k) design for given k,which are only restricted for the symmetrical case.This paper proposes and studies the clear effects problem for the asymmetrical case.It improves the construction method of Tang et al.for 2n-(n-k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components(2fic's) in 4m2n designs with resolutions III and IV.The lower bounds are achieved by constructing specific designs.Comparisons show that the number of clear 2fic's in the resulting design attains its maximum number in many cases,which reveals that the construction methods are satisfactory when they are used to construct 4m2n designs under the clear effects criterion. 相似文献
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Shakti Banerjee Bhagwandas S. Kageyama 《Annals of the Institute of Statistical Mathematics》1985,37(1):145-150
Summary Constructions of three series of regular GD and semi-regular GD designs are given. Furthermore, a series of rectangular PBIB
designs is constructed and particular cases of this series which reduce to PBIB designs with two associate classes are also
provided.
Written while visiting Department of Statistics, University of Indore, India, December 1983 through February 1984. 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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Sabine Giese 《Discrete Mathematics》2005,301(1):74-82
In the nineties, A.G. Spera introduced a construction principle for divisible designs. Using this method, we get series of divisible designs from finite Laguerre geometries. We show a close connection between some of these divisible designs and divisible designs whose construction was based on a conic in a plane of a three-dimensional projective space. 相似文献
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Snigdha Banerjee Sanpei Kageyama Bhagwandas 《Annals of the Institute of Statistical Mathematics》1987,39(1):671-679
Summary Two-associate class PBIB designs, having association schemes of GD orL
2 types, are constructed by using patterned matrices and by methods of taking unions of sets of blocks. 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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Clear effects criterion is an important criterion for selecting fractional factorial designs[1].Tang et al.[2]derived upper and lower bounds on the maximum number of clear two-factor interactions(2fi's)in 2^n-(n-k)designs of resolution Ⅲ and Ⅳ by constructing 2^n-(n-k)designs.But the method in[2]does not perform well sometimes when the resolution is Ⅲ.This article modifies the construction method for 2^n-(n-k) designs of resolution Ⅲ in[2].The modified method is a great improvement on that used in[2]. 相似文献
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Al Mingyao & HE Shuyuan Key Laborartory of Pure Applied Mathematics School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2005,48(5):649-656
The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established. 相似文献