Reliability; Multistate system; Dependent lifetimes; Semicoherent system; System joint signature
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 :
Mathematics
Author, co-author :
Marichal, J.-L.; Mathematics Research Unit, University of Luxembourg, Maison du Nombre, 6, avenue de la Fonte, Esch-sur-Alzette, Luxembourg
Mathonet, Pierre ; Université de Liège - ULiège > Département de mathématique > Géométrie différentielle
Navarro, J.; Facultad de Matemáticas, Universidad de Murcia, Murcia, Spain
Paroissin, C.; Laboratoire de Mathématiques et de leurs Applications de Pau – Fédération IPRA, CNRS / Univ Pau & Pays Adour, UMR 5142, Pau, France
Language :
English
Title :
Joint signature of two or more systems with applications to multistate systems made up of two-state components
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