Article (Scientific journals)
Joint signature of two or more systems with applications to multistate systems made up of two-state components
MARICHAL, Jean-Luc; Mathonet, Pierre; Navarro, Jorge et al.
2017In European Journal of Operational Research, 263 (2), p. 559-570
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Keywords :
Reliability; semicoherent system; dependent lifetimes; system signature; system joint signature; multistate system
Abstract :
[en] The structure signature of a system made up of n components having continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the n-tuple whose k-th coordinate is the probability that the k-th component failure causes the system to fail. More recently, a bivariate version of this concept was considered as follows. The joint structure signature of a pair of systems built on a common set of components having continuous and i.i.d. lifetimes is a square matrix of order n whose (k,l)-entry is the probability that the k-th failure causes the first system to fail and the l-th failure causes the second system to fail. This concept was successfully used to derive a signature-based decomposition of the joint reliability of the two systems. In the first part of this paper we provide an explicit formula to compute the joint structure signature of two or more systems and extend this formula to the general non-i.i.d. case, assuming only that the distribution of the component lifetimes has no ties. We also provide and discuss a necessary and sufficient condition on this distribution for the joint reliability of the systems to have a signature-based decomposition. In the second part of this paper we show how our results can be efficiently applied to the investigation of the reliability and signature of multistate systems made up of two-state components. The key observation is that the structure function of such a multistate system can always be additively decomposed into a sum of classical structure functions. Considering a multistate system then reduces to considering simultaneously several two-state systems.
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, Department of Mathematics, Liège, Belgium
Navarro, Jorge;  Facultad de Matemáticas, Universidad de Murcia, Murcia, Spain
Paroissin, Christian;  CNRS / Univ Pau & Pays Adour, Pau, France > Laboratoire de Mathématiques et de leurs Applications de Pau
External co-authors :
yes
Language :
English
Title :
Joint signature of two or more systems with applications to multistate systems made up of two-state components
Publication date :
01 December 2017
Journal title :
European Journal of Operational Research
ISSN :
1872-6860
Publisher :
Elsevier Science, Amsterdam, Netherlands
Special issue title :
Stochastics and Statistics
Volume :
263
Issue :
2
Pages :
559-570
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Security, Reliability and Trust
Name of the research project :
R-AGR-0500 - IRP15 - MRO3 (20150301-20181231) - MARICHAL Jean-Luc
Funders :
University of Luxembourg - UL
Available on ORBilu :
since 11 June 2017

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