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Limit distribution for a consecuttve-k-out-of-n: F system

Published online by Cambridge University Press:  01 July 2016

Ourania Chryssaphinou*
Affiliation:
University of Athens
Stavros G. Papastavridis*
Affiliation:
University of Patras
*
Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, 157 10, Athens.
∗∗Postal address: Department of Mathematics, University of Patras, 261 10 Patras, Greece.
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Abstract

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A consecutive-k-out-of-n: F system consists of n components ordered on a line. Each component, and the system as a whole, has two states: it is either functional or failed. The system will fail if and only if at least k consecutive components fail. The components are not necessarily equal and we assume that components' failures are stochastically independent. Using a result of Barbour and Eagleson (1984) we find a bound for the distance of the distribution of system's lifetime from the Weibull distribution. Subsequently, using this bound limit theorems are derived under quite general conditions.

Type
Letters to the Editor
Copyright
Copyright © Applied Probability Trust 1990 

References

[1] Barbour, A. D. and Eagleson, G. K. (1984) Poisson convergence for dissociated statistics. J. R. Statist. Soc. B 46, 397402.Google Scholar
[2] Chiang, D. T. and Chiang, R. F. (1986) Relayed communication via consecutive k-out-of-n: F system. IEEE Trans. Reliability 35, 65–57.CrossRefGoogle Scholar
[3] Chiang, D. T. and Niu, S. C. (1981) Reliability of consecutive k-out-of-n: F system. IEEE Trans. Reliability 30, 8789.CrossRefGoogle Scholar
[4] Derman, C., Lieberman, G. J. and Ross, S. M. (1982) On the consecutive-k-out-of-n: F system. IEEE Trans. Reliability 31, 5763.CrossRefGoogle Scholar
[5] Hwang, F. K. (1986) Simplified reliabilities for consecutive-k-out-of-n systems. SIAM J. Alg. Disc. Math. 7, 258264.CrossRefGoogle Scholar
[6] Kao, S. C. (1982) Computing reliability from warranty. Proc. Amer. Statist. Assoc. Section on Stat. Comp., 309312.Google Scholar
[7] Papastavridis, S. (1987) A limit theorem for the reliability of a consecutive-k-out-of-n: F system. Adv. Appl. Prob. 19, 746748.CrossRefGoogle Scholar
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