On the availability of R out of N repairable systems

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An R out of N repairable system consisting of N components and operates if at least R components are functioning. Repairable means that failed components are repaired, and upon repair completion they are as good as new. We derive formulas for the expected up-time, expected down-time, and the availability of the system, using Markov renewal processes. We assume that either the repair times of the components are generally distributed and the components' lifetimes are exponential or vice versa. The analysis is done for systems with either cold or warm stand-by. Numerical examples are given for several life time and repair time distributions.

Original languageEnglish
Pages (from-to)483-498
Number of pages16
JournalNaval Research Logistics
Issue number5
StatePublished - Aug 2002


  • Availability
  • Cold stand-by
  • Markov renewal process
  • R out of N systems
  • Warm stand-by

ASJC Scopus subject areas

  • Modeling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research


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