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Reliability of a consecutive-k-out-of-n system in a random environment

Published online by Cambridge University Press:  14 July 2016

Ourania Chryssaphinou  and
Stavros Papastavridis
Ourania Chryssaphinou*
Affiliation:
University of Athens
Stavros Papastavridis*
Affiliation:
University of Patras
*
∗Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece.
∗∗Postal address: Applied Mathematics Division, University of Patras, 26110 Patras, Greece.
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Abstract

We consider a consecutive-k-out-of-n system situated in a random environment where shocks occur and cause components to fail with certain probabilities. Under certain reasonable assumptions we compute the moment generating function of the time of failure of the system and the distribution of the number of shocks required to cause failure of the system.

Keywords

SHOCK MODELSFAILURE MODELSSYSTEM RELIABILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 452 - 458
Copyright
Copyright © Applied Probability Trust 1990 

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References

[1] Derman, C., Lieberman, G. J. and Ross, S. M. (1982) On the consecutive-k-out-of-n: F system. IEEE Trans. Reliability 31, 57–63.CrossRefGoogle Scholar
[2] Fu, J. C. (1985) Reliability of a large consecutive-k-out-of-n: F system. IEEE Trans. Reliability 34, 127–130.CrossRefGoogle Scholar
[3] Hwang, F. K. (1982) Fast solutions for consecutive-k-out-of-n: F system. IEEE Trans. Reliability 31, 447–448.CrossRefGoogle 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] Papastavridis, S. (1987) A limit theorem for the reliability of a consecutive-k-out-of-n system. Adv. Appl. Prob. 19, 746–748.CrossRefGoogle Scholar
[6] Råde, L. (1976) Reliability systems in random environment. J. Appl. Prob. 13, 407–410.CrossRefGoogle Scholar
[7] Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
[8] Shanthikumar, J. G. (1982) Recursive algorithm to evaluate the reliability of a consecutive-k-out-of-n: F system. IEEE Trans. Reliability 31, 442–443.CrossRefGoogle Scholar
[9] Tong, Y. L. (1985) A rearrangement inequality for the longest run with an application to network reliability. J. Appl. Prob. 22, 386–393.CrossRefGoogle Scholar