On modular decompositions of system signatures

; ;

2015 • In *Journal of Multivariate Analysis, 134*, p. 19-32

Peer reviewed

ModularDecompositionsSystemSignatures.pdf

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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

Mathematics

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

Additional URL :

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

University La Sapienza, Rome, Italy

Available on ORBilu :

since 27 October 2014

Scopus citations^{®}

16

Scopus citations^{®}

without self-citations

without self-citations

14

OpenCitations

12

WoS citations^{™}

13