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 verified by ORBi
 

Files


Full Text
ExtensionsBarlowProschan.pdf
Author postprint (139.68 kB)
Download

All documents in ORBi are protected by a user license.

Send to



Details



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 :
Mathematics
Author, co-author :
Marichal, Jean-Luc;  University of Luxembourg - UL > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Mathonet, Pierre ;  Université de Liège - ULiège > Département de mathématique > Géométrie différentielle
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
eISSN :
1095-7243
Publisher :
Academic Press
Volume :
115
Pages :
48-56
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
Unilu - Université du Luxembourg [LU]
Available on ORBi :
since 15 May 2014

Statistics


Number of views
39 (5 by ULiège)
Number of downloads
120 (2 by ULiège)

Scopus citations®
 
14
Scopus citations®
without self-citations
12
OpenCitations
 
14

Bibliography


Similar publications



Contact ORBi