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

  • Ourania Chryssaphinou (a1) and Stavros G. Papastavridis (a2)

Abstract

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.

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Copyright

Corresponding author

Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, 157 10, Athens.
∗∗Postal address: Department of Mathematics, University of Patras, 261 10 Patras, Greece.

References

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

Keywords

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

  • Ourania Chryssaphinou (a1) and Stavros G. Papastavridis (a2)

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