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A general shock model for a reliability system

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Georgios Skoulakis
Georgios Skoulakis*
Affiliation:
University of North Carolina
*
∗ Postal address: Department of Finance, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, IL 60208-20001, USA. Email address: [email protected]
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Abstract

We study a reliability system subject to shocks generated by a renewal point process. When a shock occurs, components fail independently of each other with equal probabilities that are random numbers drawn from a distribution that may differ from shock to shock. We first consider the case of a parallel system and derive closed expressions for the Laplace-Stieltjes transform and the expectation of the time to system failure and for its density in the case that the distribution function of the renewal process possesses a density. We then treat a more general system structure, which has some very important special cases, such as k-out-of-n:F systems, and derive analogous formulae.

Keywords

System reliabilityshock modelsrandom environmentparallel systemgeneral system

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K37: Processes in random environments
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 925 - 935
Copyright
Copyright © by the Applied Probability Trust 2000 

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References

[1] Chryssaphinou, O., and Papastavridis, S. (1990). Reliability of a consecutive-k-out-of-n system in a random environment. J. Appl. Prob. 27, 452–458.CrossRefGoogle Scholar
[2] Griffith, W. S. (1986). On consecutive-k-out-of-n:failure systems and their generalizations. In Reliability and Quality Control, ed. Basu, A. P. Elsevier, Amsterdam, pp. 157–165.Google Scholar
[3] Lambiris, M., and Papastavridis, S. (1985). Exact reliability formulas for linear and circular consecutive-k-out-of-n:F systems. IEEE Trans. Rel. 34, 124–126.Google Scholar
[4] Nakagawa, T. (1979). Further results of replacement problem of a parallel system in random environment. J. Appl. Prob. 16, 923–926.CrossRefGoogle Scholar
[5] Petakos, K., and Tsapelas, T. (1997). Reliability analysis for systems in a random environment. J. Appl. Prob. 34, 1021–1031.Google Scholar
[6] Råde, L. (1976). Reliability systems in random environment. J. Appl. Prob. 13, 407–410.Google Scholar
[7] Resnick, S. (1992). Adventures in Stochastic Processes. Birkhäuser, Basel.Google Scholar
[8] Ross, S. M. (1983). Stochastic Processes. John Wiley, New York.Google Scholar
[9] Srinivas, I. (1992). Distribution of the lifetime of consecutive k-within-m-out-of-n:F systems. IEEE Trans. Rel. R41, 448–450.Google Scholar