Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-21T18:40:31.105Z Has data issue: false hasContentIssue false
  • English
  • Français

A general framework for some asymptotic reliability formulas

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  01 July 2016

Christiane Cocozza-Thivent  and
Michel Roussignol
Christiane Cocozza-Thivent*
Affiliation:
Université de Marne la Vallée
Michel Roussignol*
Affiliation:
Université de Marne la Vallée
*
∗ Postal address: Equipe d'Analyse et de Mathématiques Appliquées, Université de Marne la Vallée, 5 boulevard Descartes, F-77454 Marne la Vallée Cedex 2, France.
∗ Postal address: Equipe d'Analyse et de Mathématiques Appliquées, Université de Marne la Vallée, 5 boulevard Descartes, F-77454 Marne la Vallée Cedex 2, France.
Get access Rights & Permissions [Opens in a new window]

Abstract

The authors prove that certain reliability formulas which link asymptotic availability, mean normal operation time, mean time between failures, mean number of failures over a period of time and asymptotic Vesely rate, and which are well known in the case of modelling using a Markov jump process or an alternating renewal process, are also true in the context of more general modelling.

Keywords

Semi-Markov processrenewal processreliabilityavailability

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 2 , June 2000 , pp. 446 - 467
Copyright
Copyright © Applied Probability Trust 2000 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Asmussen, S. (1992). Applied Probability and Queues. Wiley, New York.Google Scholar
[2] Barlow, R. E. and Proschan, F. (1976). Theory for maintained systems: distribution of time to first failure. Math. Operat. Res. 1, 32–42.CrossRefGoogle Scholar
[3] Cocozza-Thivent, C. (1997). Processus stochastiques et fiabilité des systèmes. Springer, Heidelberg.Google Scholar
[4] Cocozza-Thivent, C. and Kalashnikov, V. (1997). The failure rate in reliability: approximations and bounds. JAMSA 9, 497–530.Google Scholar
[5] Yeh, Lam (1997). The rate of occurrence of failures. J. Appl. Prob. 34, 234–247.CrossRefGoogle Scholar
[6] Pagès, A. and Gondran, M. (1980). Fiabilité des systèmes. Eyrolles, Collection de la Direction des Etudes et Recherches d'Electricité de France, Paris.Google Scholar
[7] Ross, S. M. (1975). On the calculation of asymptotics system reliability characteristics. Reliability and Fault Tree Analysis, eds Barlow, R. E., Fussell, J. B. and Singpurwalla, N., SIAM, Philadelphia.Google Scholar
[8] Shurenkov, V. M. (1984). On the theory of Markov renewal. Theor. Prob. Appl. 29, 247–265.CrossRefGoogle Scholar