## 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 having several repairmen. Life times of working components are i.i.d random variables having an exponential distribution. Repair times are i.i.d random variables having a phase type distribution. Both cold and warm stand-by systems are considered. We present an algorithm deriving recursively in the number of repairmen the generator of the Markov process that governs the process. Then we derive formulas for the point availability, the limiting availability, the distribution of the down time and the up time. Numerical examples are given for various repair time distributions. The numerical examples show that the availability is not very sensitive to the repair time distribution while the mean up time and the mean down time might be very sensitive to the repair time distributions.

Original language | English |
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Pages (from-to) | 202-225 |

Number of pages | 24 |

Journal | European Journal of Operational Research |

Volume | 169 |

Issue number | 1 |

DOIs | |

State | Published - 16 Feb 2006 |

## Keywords

- Down time
- Limiting availability
- Markov processes
- Phase type distributions
- Point availability
- Reliability
- Up time

## ASJC Scopus subject areas

- Computer Science (all)
- Modeling and Simulation
- Management Science and Operations Research
- Information Systems and Management