Reference : Joint signature of two or more systems with applications to multistate systems made u...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Civil engineering
Security, Reliability and Trust
http://hdl.handle.net/10993/31409
Joint signature of two or more systems with applications to multistate systems made up of two-state components
English
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mathonet, Pierre mailto [University of Liège, Department of Mathematics, Liège, Belgium]
Navarro, Jorge mailto [Facultad de Matemáticas, Universidad de Murcia, Murcia, Spain]
Paroissin, Christian mailto [CNRS / Univ Pau & Pays Adour, Pau, France > Laboratoire de Mathématiques et de leurs Applications de Pau]
1-Dec-2017
European Journal of Operational Research
Elsevier Science
263
2
Stochastics and Statistics
559-570
Yes (verified by ORBilu)
International
0377-2217
1872-6860
Amsterdam
The Netherlands
[en] Reliability ; semicoherent system ; dependent lifetimes ; system signature ; system joint signature ; multistate system
[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.
University of Luxembourg - UL
R-AGR-0500 > MRO3 > 01/03/2015 - 28/02/2018 > MARICHAL Jean-Luc
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/31409
10.1016/j.ejor.2017.06.022
http://arxiv.org/abs/1412.1613

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