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纯净效应准则是选取最优部分因析设计的重要准则之一,近年来已经成为一个活跃的研究课题.对给定的k,通过构造2n-(n-k)设计,Tang等(2002)得到了分辨度Ⅲ和ⅣV的2n-(n-k)部分因析设计的纯净两因子交互作用最大数的上下界,但是这种方法只局限于对称设计的情形.本文提出和研究了非对称情形的纯净效应问题,改进了Tang等对分辨度Ⅲ的2n-(n-k)设计的构造方法,得到了分辨度Ⅲ和ⅣV的4m2n设计的纯净两因子交互作用成分最大数的上下界,其中下界是通过构造特定的设计得到的.比较表明,本文所得设计的纯净两因子交互作用成分数在很多情形下都达到了最大.这说明在纯净效应准则下,用这些构造方法来构造4m2n设计是令人满意的. 相似文献
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纯净效应准则是选择最优部分因析设计的重要标准之一, 它已经成为近几年的一个热门研究课题. 对给定的k,文献[1]通过构造$2^{n-(n-k)}$设计, 得到了分辨度为III和IV的部分因析设计中纯净两因子交互作用最大数的上下界, 这些结果只限于对称设计的情形. 本文提出并研究了非对称设计情形的纯净效应问题. 文章改进了文献[1]对分辨度为III的$2^{n-(n-k)}$设计的构造方法, 得到了分辨度为III和IV的$4^m2^n$设计中纯净两因子交互作用成分最大数的上下界, 其中下界是通过构造特定的设计得到的. 比较结果显示所构造的设计在很多情形可以达到纯净两因子交互作用成分的最大数, 从而说明本文的构造方法在基于纯净准则构造$4^m2^n$设计方面是令人满意的. 相似文献
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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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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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讨论了(s~r)×s~n部分因子设计的估计能力问题,其中r(≥2)是一个整数,s是一个素数或素数幂.给出了(s~r)×s~n部分因子设计具有最大估计能力的一个充分条件,并证明了类型为0的最小混杂设计在估计能力准则下也是较好的设计. 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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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 2
n−(n−k) fractional factorial designs of resolutions III and IV by constructing a 2
n−(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 2
n−(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 4
m
2
n
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 4
m
2
n
designs under the clear effects criterion.
This work was supported by the National Natural Science Foundation of China (Grant Nos. 10571093, 10671099 and 10771123),
the Research Foundation for Doctor Programme (Grant No. 20050055038) and the Natural Science Foundation of Shandong Province
of China (Grant No. Q2007A05). Zhang’s research was also supported by the Visiting Scholar Program at Chern Institute of Mathematics. 相似文献
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Full factorial designs of a significant size are very rarely performed in industry due to the number of trials involved and unavailable time and resources. The data in this paper were obtained from a six‐factor full factorial (26) designed experiment that was conducted to determine the optimum operating conditions for a steel milling operation. Fractional‐factorial designs 2 (one‐eighth) and 2 (one‐fourth, using a fold‐over from the one‐eighth) are compared with the full 26 design. Four of the 2 are de‐aliased by adding four more runs. In addition, two 12‐run Plackett–Burman experiments and their combination into a fold‐over 24‐run experiment are considered. Many of the one‐eighth fractional‐factorial designs reveal some significant effects, but the size of the estimates varies much due to aliasing. Adding four more runs improves the estimation considerably. The one‐quarter fraction designs yield satisfactory results, compared to the full factorial, if the ‘correct’ parameterization is assumed. The Plackett–Burman experiments, estimating all main effects, always perform worse than the equivalent regular designs (which have fewer runs). When considering a reduced model many of the different designs are more or less identical. The paper provides empirical evidence for managers and engineers that the choice of an experimental design is very important and highlights how designs of a minimal size may not always result in productive findings. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Dong和Pei在文[Construction for de Bruijn sequences with large stage,Des.Codes Cryptogr,2017,85(2):343-358]中利用F_2[x]的n次不可约多项式构造大级数de Bruijn序列.不可约多项式的邻接矩阵从理论上给出了这种方法能构造de Bruijn序列的数目.我们给出一类特殊不可约多项式的邻接矩阵,从理论上给出了用这类不可约多项式能够构造的de Bruijn序列的数目. 相似文献
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Fractional factorial designs (FFD’s) are no doubt the most widely used designs in the experimental investigations due to their efficient use of experimental runs to study many factors simultaneously. One consequence of using FFD’s is the aliasing of factorial effects. Follow-up experiments may be needed to break the confounding. A simple strategy is to add a foldover of the initial design, the new fraction is called a foldover design. Combining a foldover design with the original design converts a design of resolution r into a combined design of resolution \(r+1\). In this paper, we take the centered \(L_2\)-discrepancy \(({\mathcal {CD}})\) as the optimality measure to construct the optimal combined design and take asymmetrical factorials with mixed two and three levels, which are most commonly used in practice, as the original designs. New and efficient analytical expressions based on the row distance of the \({\mathcal {CD}}\) for combined designs are obtained. Based on these new formulations, we present new and efficient lower bounds of the \({\mathcal {CD}}\). Using the new formulations and lower bounds as the benchmarks, we may implement a new algorithm for constructing optimal mixed-level combined designs. By this search heuristic, we may obtain mixed-level combined designs with low discrepancy. 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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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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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 resolution III or IV under 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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设f,g是两个非常数亚纯函数,a是一个非零有穷复数,n≥5是一个正整数.若[f(z)]~n与[g(z)]~n CM分担a,f(z)与g(z) CM分担∞,且N_(1))(r,f)=S(r,f),则或者f(z)三tg(z),其中t~n=1;或者f(z)g(z)≡t,其中t~n=a~2.由此改进了涉及导数与差分的一些亚纯函数唯一性的结果. 相似文献