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

Yonit Barron, Esther Frostig, Benny Levikson

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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 languageEnglish
Pages (from-to)116-138
Number of pages23
JournalAdvances in Applied Probability
Issue number1
StatePublished - Mar 2004
Externally publishedYes


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


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