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On the availability of R out of N repairable systems

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  • Esther Frostig
  • Benny Levikson

Abstract

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. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 483–498, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10025

Suggested Citation

  • Esther Frostig & Benny Levikson, 2002. "On the availability of R out of N repairable systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(5), pages 483-498, August.
    • Handle: RePEc:wly:navres:v:49:y:2002:i:5:p:483-498
    DOI: 10.1002/nav.10025
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    References listed on IDEAS

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    1. Smith, M. A. J. & Dekker, R., 1997. "Preventive maintenance in a 1 out of n system: The uptime, downtime and costs," European Journal of Operational Research, Elsevier, vol. 99(3), pages 565-583, June.
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