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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.
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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 

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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