Article (Scientific journals)
On modular decompositions of system signatures
; ;
2015In Journal of Multivariate Analysis, 134, p. 19-32
Peer reviewed

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#### Details

Keywords :
System signature; tail signature; semicoherent system; modular decomposition
Abstract :
[en] Considering a semicoherent system made up of \$n\$ components having i.i.d. continuous lifetimes, Samaniego defined its structural signature as the \$n\$-tuple whose \$k\$-th coordinate is the probability that the \$k\$-th component failure causes the system to fail. This \$n\$-tuple, which depends only on the structure of the system and not on the distribution of the component lifetimes, is a very useful tool in the theoretical analysis of coherent systems. It was shown in two independent recent papers how the structural signature of a system partitioned into two disjoint modules can be computed from the signatures of these modules. In this work we consider the general case of a system partitioned into an arbitrary number of disjoint modules organized in an arbitrary way and we provide a general formula for the signature of the system in terms of the signatures of the modules. The concept of signature was recently extended to the general case of semicoherent systems whose components may have dependent lifetimes. The same definition for the \$n\$-tuple gives rise to the probability signature, which may depend on both the structure of the system and the probability distribution of the component lifetimes. In this general setting, we show how under a natural condition on the distribution of the lifetimes, the probability signature of the system can be expressed in terms of the probability signatures of the modules. We finally discuss a few situations where this condition holds in the non-i.i.d. and nonexchangeable cases and provide some applications of the main results.
Disciplines :
Civil engineering
Mathematics
Author, co-author :
Marichal, Jean-Luc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Mathonet, Pierre;  University of Liège, Belgium > Department of Mathematics
Spizzichino, Fabio;  University La Sapienza, Rome, Italy > Department of Mathematics
External co-authors :
yes
Language :
English
Title :
On modular decompositions of system signatures
Publication date :
February 2015
Journal title :
Journal of Multivariate Analysis
ISSN :
0047-259X
Publisher :
Elsevier
Volume :
134
Pages :
19-32
Peer reviewed :
Peer reviewed
Focus Area :
Security, Reliability and Trust
Name of the research project :
F1R-MTH-PUL-12RDO2 > MRDO2 > 01/02/2012 - 28/02/2015 > MARICHAL Jean-Luc
Funders :
University of Luxembourg - UL
University La Sapienza, Rome, Italy
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