Birnbaum importance measure of network based on C-spectrum under saturated poisson distribution

Y. J. Du, S. B. Si, H. Y. Gao, Z. Q. Cai

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Importance measures usually provide numerical indicator to decide which component is more important for network reliability improvement or more critical for network failure. The concept of C-spectrum is a useful tool to implement the importance measures for network, which solely depends on network structure. In this paper, we analyze a network that consists of n components (edges). Under the condition that the distribution of the number of failed edges is given, the properties of traditional Birnbaum importance measure (BIM) are generalized and investigated. First, we derive a formula for BIM based on C-spectrum and establish a sufficient and necessary condition for comparing two edges according to their BIMs. Secondly, under the special case where the number of failed edges follows a saturated Poisson distribution with intensity λ, for enough small λ the BIM ranking is structural ranking, i.e., depending solely on the network structure through the C-spectrum. Finally, an example is presented to explain how we can rank edges according to their BIMs.

Original languageEnglish
Title of host publication2017 IEEE International Conference on Industrial Engineering and Engineering Management, IEEM 2017
PublisherIEEE Computer Society
Pages934-938
Number of pages5
ISBN (Electronic)9781538609484
DOIs
StatePublished - 2 Jul 2017
Event2017 IEEE International Conference on Industrial Engineering and Engineering Management, IEEM 2017 - Singapore, Singapore
Duration: 10 Dec 201713 Dec 2017

Publication series

NameIEEE International Conference on Industrial Engineering and Engineering Management
Volume2017-December
ISSN (Print)2157-3611
ISSN (Electronic)2157-362X

Conference

Conference2017 IEEE International Conference on Industrial Engineering and Engineering Management, IEEM 2017
Country/TerritorySingapore
CitySingapore
Period10/12/1713/12/17

Keywords

  • Birnbaum importance measure
  • C-spectrum
  • network
  • saturated Poisson distribution

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