Approximation of Reliability for a large system with non-markovian repair-times

Free access article

Issue		ESAIM: PS Volume 3, 1999


Page(s)		49 - 65
DOI		10.1051/ps:1999102

DOI: 10.1051/ps:1999102

ESAIM: PS, June 1999, Vol. 3, p. 49-65

Approximation of Reliability for a large system with non-markovian repair-times

Approximation de la fiabilité des grands systèmes avec réparation non-exponentielle

Jean-Louis Bon and Jean Bretagnolle
Laboratoire de Modélisation Stochastique et Statistique, bâtiment 425, Université Paris-Sud, 91405 Orsay Cedex, France;
(jean-louis.bon@math.u-psud.fr) and (jean.bretagnolle@math.u-psud.fr)

Received January 10, 1998. Revised January 25, 1999

Abstract: Consider a system of many components with constant failure rate and general repair rate. When all components are reliable and easily reparable, the reliability of the system can be evaluated from the probability q of failure before restoration. In [14], authors give an asymptotic approximation by monotone sequences. In the same framework, we propose, here, a bounding for q and apply it in the ageing property case.

Résumé: Le calcul de la fiabilité d'un grand système réparable peut être réduit à celui de la probabilité q de panne avant remise à neuf. Dans [14], les auteurs donnent une approximation asymptotique de q par séquences monotones pour un système k/n. Nous proposons ici un encadrement de q dans un cadre plus général et l'appliquons à des réparations vieillissantes.

Keywords and phrases: Reliability, ageing repair, minimal cut.

AMS Subject Classification: 62N05, 90B25, 60K

Article without figures.

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