Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-07-07T15:17:32.875Z Has data issue: false hasContentIssue false
  • English
  • Français

The Downtime Distribution After a Failure of a System with Multistate Independent Components

Part of: Distribution theory Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Antonio Pievatolo
Antonio Pievatolo*
Affiliation:
IMATI-CNR
*
∗Postal address: IMATI-CNR, via Bassini 15, 20133 Milano, Italy. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Aven and Jensen (1999) proposed an approximation to the downtime distribution for arbitrary coherent systems with binary and independent repairable components, where each component follows an alternating renewal process. The approximation is based on a mixture of the duration distributions of the cut sets in the system. We extend this approach to coherent systems composed by multistate independent components, where every component follows a semi-Markov process and where we introduce the concept of a minimal cut set in the multistate setting. We test our proposal on a simple power demand-generation system, by comparing the analytic approximation with simulation results, and we find it is accurate when the system is highly available.

Keywords

Semi-Markov processcut setmixture distribution

MSC classification

Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) 62E17: Approximations to distributions (nonasymptotic) 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 1068 - 1077
Copyright
Copyright © Applied Probability Trust 2007 

References

[1] Aven, T. and Jensen, U. (1999). Stochastic Models in Reliability. Springer, New York.Google Scholar
[2] Çinlar, E. (1975). Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
[3] Gåsemyr, J. and Aven, T. (1999). Asymptotic distributions for the downtime of monotone systems. J. Appl. Prob. 36, 814–829.Google Scholar
[4] Lisnianski, A. and Levitin, G. (2003). Multi-state System Reliability. World Scientific, Singapore.Google Scholar
[5] Pievatolo, A., Tironi, E. and Valadè, I. (2004). Semi-Markov processes for power system reliability assessment with application to uninterruptible power supply. IEEE Trans. Power Systems 19, 1326–1333.Google Scholar
[6] Ross, S. M. (1970). Applied Probability Models with Optimization Applications. Holden Day, San Francisco, CA.Google Scholar
[7] Van Casteren, J. F. L., Bollen, M. H. J. and Schmieg, M. E. (2000). Reliability assessment in electrical power systems: the Weibull–Markov stochastic model. IEEE Trans. Ind. Appl. 36, 911–915.CrossRefGoogle Scholar