## 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.

Original language | English |
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Pages (from-to) | 116-138 |

Number of pages | 23 |

Journal | Advances in Applied Probability |

Volume | 36 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2004 |

## Keywords

- Availability
- Down time
- Markov renewal process
- Phase-type distribution
- Regenerative point
- Semi-regenerative point
- Up time

## ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics