|
|
论文:2017,Vol:35,Issue(5):870-875 |
|
|
引用本文： |
|
|
杜永军, 侯沛勇, 郭雅琪. 基于饱和泊松分布的网络边的Birnbaum重要度计算方法[J]. 西北工业大学学报 |
|
|
Du Yongjun, Hou Peiyong, Guo Yaqi. Network Birnbaum Importance Measure under Saturated Poisson Distribution[J]. Northwestern polytechnical university |
|
|
|
|
|
|
|
| 基于饱和泊松分布的网络边的Birnbaum重要度计算方法 |
|
| 杜永军1,2, 侯沛勇1, 郭雅琪1 |
|
1. 西北工业大学 机电学院, 陕西 西安 710072;
2. 兰州理工大学 理学院, 甘肃 兰州 730050 |
| 摘要: |
| 重要度是系统可靠性领域用以识别系统薄弱环节的主要方法之一，也是系统可靠性优化的前提和基础。在对传统Birnbaum重要度计算方法研究的基础上，假设网络边故障个数概率分布已知的前提下，基于网络结构谱，给出了一种基于概率分布的Birnbaum重要度计算方法，重点探讨了网络故障边个数服从饱和泊松分布时Birnbaum重要度的性质。最后，结合算例给出了基于饱和泊松分布的Birnbaum重要度的应用方法。 |
| 关键词:
网络
Birnbaum重要度
饱和泊松分布
网络结构谱
|
|
| Network Birnbaum Importance Measure under Saturated Poisson Distribution |
|
| Du Yongjun1,2, Hou Peiyong1, Guo Yaqi1 |
|
1. School of Mechatronics, Northwestern Polytechnical University, Xi'an 710072, China;
2. School of Science, Lanzhou University of Technology, Lanzhou 730050, China |
| Abstract: |
| Network reliability analysis aim to quantify the impact of component failures on the network failure and to identify the weakness in a network. Importance measures provides numerical indicator to determine which components are more important for network reliability improvement or more critical for network failure. In this paper, the number of failed components is introduced, which is a random variable having a distribution. Under the condition of the distribution have been known, based on the structural spectrum, a new method to compute Birnbaum importance measure is derived. In particularly, when the number of failed components follows a saturated Poisson distribution, several results concerning ranking of components according to Birnbaum importance measure is presented. Finally, an example is presented to explain the application of the results. |
| Key words:
Birnbaum importance measure
D-spectrum
network
saturated Poisson distribution
|
|
| 收稿日期: 2017-03-20
修回日期:
|
| DOI: |
| 基金项目: 国家自然科学基金（7147147）和高等学校学科创新引智计划（B13044）资助 |
| 通讯作者: 侯沛勇(1964-),西北工业大学副教授、博士,主要从事系统工程与管理研究。
Email： |
| 作者简介: 杜永军(1977-),西北工业大学博士研究生,主要从事网络可靠性及网络重要度研究。
|
|
|
|
|
|
|
|
参考文献: |
|
|
[1] Birnbaum Z W. On the Importance of Different Components in a Multicomponent System//Multivariate AnalysisⅡ[M]. Ed by Krishnaiahp R. New York, Academic Press, 1969:581-592
[2] Barlow R E, Proschan F. Importance of System Components and Fault Tree Events[J]. Stochastic Processes and Their Applications, 1975, 3(2):153-173
[3] Vesely W E. A Time-Dependent Methodology for Fault Tree Evaluation[J]. Nuclear Engineering and Design, 1970, 13(2):337-360
[4] Fussell J B. How to Hand-Calculate System Reliability and Safety Characteristics[J]. IEEE Trans on Reliability, 1975, 24(3):169-174
[5] Vasseur D, Llory M. International Survey on Psa Figures of Merit[J]. Reliability Engineering & System Safety, 1999, 66(3):261-274
[6] Levitin G, Podofillini L, Zio E. Generalised Importance Measures for Multi-State Elements Based on Performance Level Restrictions[J]. Reliability Engineering & System Safety, 2003, 82(3):287-298
[7] Kuo W, Zuo M J. Optimal Reliability Modeling:Principles and Applications[M]. New York, John Wiley &Sons, 2003
[8] Shen K, Xie M. On the Increase of System Reliability by Parallel Redundancy[J]. IEEE Trans on Reliability, 1990, 39(5):607-611
[9] Singpurwalla N D. Reliability and Risk:A Bayesian Perspective[M]. New York, Join Wiley & Sons, 2006
[10] 司书宾,杨柳,蔡志强,等. 二态系统组(部)件综合重要度计算方法研究[J]. 西北工业大学学报, 2011, 29(06):939-947 Si Shubin, Yang Liu, Cai Zhiqiang, et al. A New and Eficient Computation Method of Im (Integrated Importance Measures) for Components in Binary Coherent Systems[J]. Journal of Northwestern Polytechnical University, 2011, 29(6):939-947(in Chinese)
[11] Si S B, Dui H Y, Cai Z Q, et al. Joint Integrated Importance Measure for Multi-State Transition Systems[J]. Communications in Statistics-Theory and Methods, 2012, 41(21):3846-3862
[12] 涂慧玲,张胜贵,司书宾,等. 面向维修过程的多态混联系统综合重要度计算方法[J]. 自动化学报, 2014, 40(01):126-134 Tu Huiling, Zhang Shenggui, Si Shubin, et al. The Integrated Importance Measure of Multi-State Compound Systems for Maintenance Processes[J]. Acta Automatica Sinica, 2014, 40(1):126-134(in Chinese)
[13] Page L B, Perry J E. Reliability Polynomials and Link Importance in Networks[J]. IEEE Trans on Reliability, 1994, 43(1):51-58
[14] Gertsbakh I, Shpungin Y. Network Reliability Importance Measures:Combinatories and Monte Carlo Based Computations[J]. WSEAS Transactions on Computers, 2008, 7(4):216-227
[15] Hong J S,Lie C H. Joint Reliability-Importance of Two Edges in an Undirected Network[J]. IEEE Trans on Reliability, 1993, 42(1):17-23
[16] Gertsbakh I B,Shpungin Y. Combinatorial Approach to Computing Component Importance Indexes in Coherent Systems[J]. Probability in the Engineering and Informational Sciences, 2012, 26(1):117-128
[17] Hsu S J,Yuang M C. Efficient Computation of Marginal Reliability Importance for Reducible Networks in Network Management[C]//Proceedings of the 1999 IEEE International Conference on Communications, 1999:1039-1045
[18] Vaisman R, Kroese D P, Gertsbakh I B. Improved Sampling Plans for Combinatorial Invariants of Coherent Systems[J]. IEEE Trans on Reliability, 2016, 65(1):410-424
[19] Kim J, Dobson I. Approximating a Loading-Dependent Cascading Failure Model with a Branching Process[J]. IEEE Trans on Reliability, 2010, 59(4):691-699 |
|
|
|
|
|
|
|
