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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)


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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Postal address: Department of Statistics, University of Haifa, Haifa 31905, Israel.
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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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