劉民千
個性化簽名
 姓名：劉民千
 目前身份：
 擔任導師情況：
 學位：

學術頭銜：
教育部“新世紀優秀人才支持計劃”入選者， 博士生導師
 職稱：

學科領域：
數理統計學
 研究興趣：
40262.9679514

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13
【期刊論文】Weak minimum aberration and maximum number of clear twofactor interactions in 2IVm?p designs
劉民千， YANG Guijun ， LIU Minqian & ZHANG Runchu
Science in China Ser. A Mathematics 2005 Vol. 48 No.11 14791487，0001，（）：
1年11月30日
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 twofactor interactions in the designs. And some conditions are provided, under which a 2IVm?p design can have the maximum number of clear twofactor interactions and weak minimum aberration at the same time. Some weak minimum aberration 2IVm?p designs are provided for illustrations and two nonisomorphic weak minimum aberration 2IV13?6 designs are constructed at the end of this paper.
clear,， weak minimum aberration,， resolution,， wordlength pattern.，

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【期刊論文】Some results on resolvable incomplete block designs
劉民千， LIU Minqian & FANG Kaitai
Science in China Ser. A Mathematics 2005 Vol. 48 No.4 503512，0001，（）：
1年11月30日
This paper is concerned with the uniformity of a certain kind of resolvable incomplete block (RIB for simplicity) design which is called the PRIB design here. A sufficient and necessary condition is obtained, under which a PRIB design is the most uniform in the sense of a discrete discrepancy measure, and the uniform PRIB design is shown to be connected. A construction method for such designs via a kind of Utype designs is proposed, and an existence result of these designs is given. This method sets up an important bridge between PRIB designs and Utype designs.
block design,， discrepancy,， orthogonal array,， supersaturated design,， Utype design.，

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【期刊論文】Construction of Uniform Designs via Supersimple Resolvable tdesigns*
劉民千， KaiTai Fang a， GenNian Ge b， MinQian Liu c， Hong Qind， a
Utilitas Mathematica 66 (2004), pp. 1532，0001，（）：
1年11月30日
A uniform design seeks design points that axe uniformly scattared on the experimental domain. It has been popular since 1980. In this paper, we employ the discrete discrepancy as the measure of uniformity for constructing uniform designs. The equivalency among the discrete discrepancy, nonorthogonal measure E (fNoo) and minimum generalized aberration (MGA) for comparing Utype designs U(n; qm) is given. The link between the two apparently unrelated areas of uniform designs and supersimple resolvable Ldesigns in combinatorial design theory is shown. Through supersimple resolvable tdesigns, under the discrete discrepancy, a new method is proposed for constructing uniform designs Un (q,m), in which any of the q2 levelcombinations between any two distinct columns can appear at most twice and any two columns are not fully aliased. Many new uniform designs are obtained.
MGA， nearly orthogonal design， resolvable tdesign， supersimple， uniform design， Utype design

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【期刊論文】Some theory and the construction of mixedlevel supersaturated designs
劉民千， PengFei Li， MinQian Liu*， RunChu Zhang
Statistics & Probability Letters 69(2004)105116，0001，（）：
1年11月30日
Supersaturated design is a form of fractional factorial design and has recently received much interest because of its potential in factor screening experiments. This paper mainly concerns the existing criteria for mixedlevel designs, i.e. the x2(D) criterion (for design D) proposed by Yamada and Matsui (J. Statist.Plann. Inference 104 (2002) 459), the E (fNOD) criterion proposed by Fang et al. (Metrika 58 (2003b) 279) and the minimum moment aberration (MMA) proposed by Xu (Statist. Sinica 13 (2003) 691). A lower bound of x2(D) is obtained along with the sufficient and necessary condition for achieving it. The connections between x2(D) and other criteria are discussed. Especially, it is shown that x2(D) and the second power moment x2(D) are in fact equivalent to each other and hence the two criteria, x2(D) and MMA, share the same optimal supersaturated designs, which can be constructed from saturated orthogonal arrays and other supersaturated designs.
Factorial design， Orthogonal array， Minimum moment aberration， Supersaturated design， Utype design

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【期刊論文】Uniformity of incomplete block designs
劉民千， MinQian Liu， LingYau Chan
Int. J. Materials and Product Technology, Vol. 20, Nos. 13, 2004，0001，（）：
1年11月30日
Incomplete block designs are a type of experimental design layout that has had widespread use in science and engineering. A balanced incomplete block design (BIB) can be characterized by the balanced arrangement of its design points. In this article, incomplete block designs will be investigated from a new perspective: the perspective of uniformity in distribution of design points. A design is of high uniformity, or low discrepancy, if its design points distribute uniformly over the entire design space. The authors use a general discrepancy measure to prove theoretically that BIBs are the most uniform ones among all binary incomplete block designs.
balanced incomplete block design， uniformity， uniform design， discrepancy.，

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【期刊論文】Construction of optimal supersaturated designs by the packing method
劉民千， FANG Kaitai ， GE Gennian & LIU Minqian
Science in China Ser. A Mathematics 2004 Vol. 47 No.1 128143，0001，（）：
1年11月30日
A supersaturated design is essentially a factorial design with the equal occurrence of levels property and no fully aliased factors in which the number of main effects is greater than the number of runs. It has received much recent interest because of its potential in factor screening experiments. A packing design is an important object in combinatorial design theory. In this paper, a strong link between the two apparently unrelated kinds of designs is shown. Several criteria for comparing supersaturated designs are proposed, their properties and connections with other existing criteria are discussed. A combinatorial approach, called the packing method, for constructing optimal supersaturated designs is presented, and properties of the resulting designs are also investigated. Comparisons between the new designs and other existing designs are given, which show that our construction method and the newly constructed designs have good properties.
Kirkman triple systems,， orthogonality,， packing design,， resolvability,， supersaturated design.，

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【期刊論文】Combinatorial constructions for optimal supersaturated designs
劉民千， KaiTai Fang a， Gennian Ge b， *， MinQian Liu c， Hong Qin d， a
Discrete Mathematics 279(2004)191202，0001，（）：
1年11月30日
Combinatorial designs have long had substantial application in the statistical design ofexperiments, and in the theory oferrorcorrecting codes. Applications in experimental and theoretical computer science, communications, cryptography and networking have also emerged in recent years. In this paper, we focus on a new application of combinatorial design theory in experimental design theory. E(fNOD) criterion is used as a measure ofnonorthogonality ofUtype designs, and a lower bound of E(fNOD) which can serve as a benchmark ofdesign optimality is obtained. A Utype design is E(fNOD)optimal ifits E(fNOD) value achieves the lower bound. In most cases, E(fNOD)optimal Utype designs are supersaturated. We show that a kind of E(fNOD)optimal designs are equivalent to uniformly resolvable designs. Based on this equivalence, several new in<nite classes for the existence of E(fNOD)optimal designs are then obtained.
Block design， Incidence matrix， Supersaturated design， Uniformly resolvable design， Utype design

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【期刊論文】Optimal mixedlevel supersaturated design
劉民千， KaiTai Fang ， Dennis K. J. Lin and MinQian Liu
Metrika (2003) 58: 279291，0001，（）：
1年11月30日
A supersaturated design is essentially a fractional factorial in which the number of potential effects is greater than the number of runs. In this paper, EefNODT criterion is employed for comparing supersaturated designs from the viewpoint of orthogonality and uniformity, and a lower bound of EefNODT which can serve as a benchmark of design optimality is obtained. It is shown that the existing Ees2T and ave v2 criteria (for two and threelevel supersaturated designs respectively) are in fact special cases of this criterion. Furthermore, a construction method for mixedlevel supersaturated designs is proposed and some properties of the resulting designs are investigated.
Discrepancy， Hamming distance， Orthogonal array， Supersaturated design， Uniformity， Utype design.，

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【期刊論文】Construction of minimum generalized aberration designs
劉民千， KaiTai Fang ， GenNian Ge ， MinQian Liu ， Hong Qin ，
Metrika (2003) 57: 3750，0001，（）：
1年11月30日
Supersaturated designs have become increasingly popular in recent years because of their potential in saving run size and the technical novelty. In this paper, the minimum generalized aberration (MGA) criterion proposed by Ma and Fang (2001) (and another two equivalent criteria proposed by Xu and Wu (2001) and Xu (2001b) respectively) for comparing nonregular symmetrical designs is used for evaluating supersaturated designs. A new construction method for MGA symmetrical supersaturated designs via resolvable balanced incomplete block designs is proposed, and some infinite classes for the existence of such MGA designs are obtained simultaneously, along with the investigation of properties of the resulting designs. The construction method shows a strong connection between these two different kinds of designs.
generalized wordlength pattern,， minimum generalized aberration,， nonregular design,， parallel class,， resolvable balanced incomplete block design,， supersaturated design

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【期刊論文】Uniform supersaturated design and its construction
劉民千， FANG Kaitai， GE Gennian & LIU Minqian
SCIENCE IN CHINA (Series A) August 2002 Vol. 45 No.8，0001，（）：
1年11月30日
Supersaturated designs are factorial designs in which the number of main e ects is greater than the number of experimental runs. In this paper, a discrete discrepancy is proposed as a measure of uniformity for supersaturated designs, and a lower bound of this discrepancy is obtained as a benchmark of design uniformity. A construction method for uniform supersaturated designs via resolvable balanced incomplete block designs is also presented along with the investigation of properties of the resulting designs. The construction method shows a strong link between these two di erent kinds of designs.
discrepancy,， resolvable balanced incomplete block design,， supersaturated design,， uniformity.，

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