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Analysis of R-out-of-N repairable systems: the case of phase-type distributions

  • Yonit Barron (a1), Esther Frostig (a1) and Benny Levikson (a1)

Abstract

An R-out-of-N repairable system, consisting of N independent components, is operating if at least R components are functioning. The system fails whenever the number of good components decreases from R to R-1. A failed component is sent to a repair facility. After a failed component has been repaired it is as good as new. Formulae for the availability of the system using Markov renewal and semi-regenerative processes are derived. We assume that either the repair times of the components are generally distributed and the components' lifetimes are phase-type distributed or vice versa. Some duality results between the two systems are obtained. Numerical examples are given for several distributions of lifetimes and of repair times.

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Corresponding author

Postal address: Department of Statistics, University of Haifa, Haifa 31905, Israel.
∗∗ Email address: frostig@stat.haifa.ac.il

References

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Asmussen, S. (2000). Ruin Probabilities (Adv. Ser. Statist. Sci. Appl. Prob. 2). World Scientific, River Edge, NJ.
Assaf, D. and Levikson, B. (1982). Closure of phase type distributions under operations arising in reliability theory. Ann. Prob. 10, 265269.
Aven, T. and Jensen, U. (1998). Stochastic Models in Reliability (Appl. Math. 41). Springer, New York.
Çinlar, E., (1975). Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs, NJ.
Fawzi, B. B. and Hawkes, A. G. (1991). Availability of an R-out-of-N system with spares and repairs. J. Appl. Prob. 28, 397408.
Frostig, E. and Levikson, B. (2002). On the availability of R out of N repairable system. Naval Res. Logistics 49, 483498. Society for Industrial and Applied Mathematics, Philadelphia, PA.
Neuts, M. F. (1975). Probability distributions of phase type. In Liber Amicorum Professor Emeritus H. Florin. Department of Mathematics, University of Louvain, pp. 173206.
Neuts, M. F. (1981). Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD.
Neuts, M. F. and Takahashi, Y. (1981). Asymptotic behavior of the stationary distributions in the GI/PH/c queue with heterogenous servers. Z. Wahrscheinlichkeitsth. 57, 441452.
Neuts, M. F., Pérez-Ocón, R. and Torres-Castro, I. (2000). Repairable models with operating and repair times governed by phase type distributions. Adv. Appl. Prob. 32, 468479.
Ross, S. M. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.

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Analysis of R-out-of-N repairable systems: the case of phase-type distributions

  • Yonit Barron (a1), Esther Frostig (a1) and Benny Levikson (a1)

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