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Convergence of the number of failed components in a Markov system with nonidentical components

Part of: Operations research and management science Special processes Markov processes Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Jean-Louis Bon  and
Eugen Păltănea
Jean-Louis Bon*
Affiliation:
Université Lille-1
Eugen Păltănea
Affiliation:
Université Paris-Sud
*
∗ Postal address: Université Lille-1 EUDIL, Département GIS, Cité Scientifique, 59655 Villeneuve d'Ascq cedex, France. Email address: [email protected]
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Abstract

For most repairable systems, the number N(t) of failed components at time t appears to be a good quality parameter, so it is critical to study this random function. Here the components are assumed to be independent and both their lifetime and their repair time are exponentially distributed. Moreover, the system is considered new at time 0. Our aim is to compare the random variable N(t) with N(∞), especially in terms of total variation distance. This analysis is used to prove a cut-off phenomenon in the same way as Ycart (1999) but without the assumption of identical components.

Keywords

Markovreliabilityavailabilitycut-offtotal variation

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K10: Applications (reliability, demand theory, etc.) 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 882 - 897
Copyright
Copyright © by the Applied Probability Trust 2001 

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Footnotes

∗∗

Current address: Universitatea Transilvania, 2200 Brasov, Romania.

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