Reference : Probability signatures of multistate systems made up of two-state components

	Document type :	Scientific congresses, symposiums and conference proceedings : Unpublished conference
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics Engineering, computing & technology : Civil engineering
	Focus Areas :	Security, Reliability and Trust
	To cite this reference:	http://hdl.handle.net/10993/31679

Title :	Probability signatures of multistate systems made up of two-state components
Language :	English
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]
	Jorge, Navarro [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]
Publication date :	Jul-2017
Peer reviewed :	Yes
On invitation :	No
Audience :	International
Event name :	10th International Conference on Mathematical Methods in Reliability (MMR 2017)
Event date :	from 03-07-2017 to 06-07-2017
Event organizer :	Olivier Gaudoin (General chair)
Event place (city) :	Grenoble
Event country :	France
Keywords :	[en] 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 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.
Target :	Researchers ; Professionals ; Students
Permalink :	http://hdl.handle.net/10993/31679
Other URL :	http://mmr2017.imag.fr/

	File(s) associated to this reference
	Fulltext file(s): File Commentary Version Size Access Open access MMR_2017_MMNPV4.pdf Author postprint 236.82 kB View/Open Additional material(s): File Commentary Size Access Open access TalkMMR.pdf Slides 963.78 kB View/Open

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