Reference : Probability signatures of multistate systems made up of two-state components
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Probability signatures of multistate systems made up of two-state components
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]
Jorge, Navarro 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]
10th International Conference on Mathematical Methods in Reliability (MMR 2017)
from 03-07-2017 to 06-07-2017
Olivier Gaudoin (General chair)
[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 this talk we will show 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. Then we will discuss a condition on this distribution for the joint reliability of the systems to have a signature-based decomposition. Finally we will show how these results can be applied to the investigation of the reliability and signature of multistate systems made up of two-state components.
Researchers ; Professionals ; Students

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