Article (Scientific journals)
On the extensions of Barlow-Proschan importance index and system signature to dependent lifetimes
Marichal, Jean-Luc; Mathonet, Pierre
2013In Journal of Multivariate Analysis, 115, p. 48-56
Peer reviewed
 

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Keywords :
Coherent system; Component importance; Barlow-Proschan index; Dependent lifetimes; System signature
Abstract :
[en] For a coherent system the Barlow-Proschan importance index, defined when the component lifetimes are independent, measures the probability that the failure of a given component causes the system to fail. Iyer (1992) extended this concept to the more general case when the component lifetimes are jointly absolutely continuous but not necessarily independent. Assuming only that the joint distribution of component lifetimes has no ties, we give an explicit expression for this extended index in terms of the discrete derivatives of the structure function and provide an interpretation of it as a probabilistic value, a concept introduced in game theory. This enables us to interpret Iyer's formula in this more general setting. We also discuss the analogy between this concept and that of system signature and show how it can be used to define a symmetry index for systems.
Research center :
Mathematics Research Unit
Disciplines :
Civil engineering
Mathematics
Identifiers :
UNILU:UL-ARTICLE-2012-1111
Author, co-author :
Marichal, Jean-Luc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Mathonet, Pierre ;  University of Liège > Department of Mathematics
External co-authors :
yes
Language :
English
Title :
On the extensions of Barlow-Proschan importance index and system signature to dependent lifetimes
Publication date :
March 2013
Journal title :
Journal of Multivariate Analysis
ISSN :
0047-259X
Publisher :
Elsevier
Volume :
115
Pages :
48-56
Peer reviewed :
Peer reviewed
Focus Area :
Security, Reliability and Trust
Name of the research project :
F1R-MTH-PUL-12RDO2 > MRDO2 > 01/02/2012 - 31/01/2015 > MARICHAL Jean-Luc
Funders :
University of Luxembourg - UL
Available on ORBilu :
since 14 May 2013

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