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Computing limiting average availability of a repairable system through discretization

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  • Chatterjee, Debolina
  • Sarkar, Jyotirmoy

Abstract

Formulas for limiting average availability of a repairable system exist only for some special cases: (1) either the lifetime or the repair time is exponential; or (2) there is one spare unit and one repair facility. We consider a more general setting involving several spare units and several repair facilities; and we allow arbitrary life- and repair time distributions. Under periodic monitoring, which essentially discretizes the time variable, we compute the limiting average availability. The discretization approach closely approximates the existing results in the special cases; and increases the limiting average availability as we include additional spare unit or additional repair facility.

Suggested Citation

  • Chatterjee, Debolina & Sarkar, Jyotirmoy, 2020. "Computing limiting average availability of a repairable system through discretization," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:reensy:v:193:y:2020:i:c:s0951832019303801
    DOI: 10.1016/j.ress.2019.106616
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    References listed on IDEAS

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    1. Sarkar, Jyotirmoy & Li, Fang, 2006. "Limiting average availability of a system supported by several spares and several repair facilities," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1965-1974, December.
    2. Sarkar, Jyotirmoy & Sarkar, Sahadeb, 2001. "Availability of a periodically inspected system supported by a spare unit, under perfect repair or perfect upgrade," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 207-217, June.
    3. Biswas, Atanu & Sarkar, Jyotirmoy, 2000. "Availability of a system maintained through several imperfect repairs before a replacement or a perfect repair," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 105-114, November.
    4. de Smidt-Destombes, Karin S. & van der Heijden, Matthieu C. & van Harten, Aart, 2007. "Availability of k-out-of-N systems under block replacement sharing limited spares and repair capacity," International Journal of Production Economics, Elsevier, vol. 107(2), pages 404-421, June.
    5. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2017. "Optimal loading of series parallel systems with arbitrary element time-to-failure and time-to-repair distributions," Reliability Engineering and System Safety, Elsevier, vol. 164(C), pages 34-44.
    6. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2015. "Optimal loading of system with random repair time," European Journal of Operational Research, Elsevier, vol. 247(1), pages 137-143.
    7. Sarkar, Jyotirmoy & Chaudhuri, Gopal, 1999. "Availability of a system with gamma life and exponential repair time under a perfect repair policy," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 189-196, June.
    8. Levitin, Gregory & Xing, Liudong & Huang, Hong Zhong, 2019. "Dynamic availability and performance deficiency of common bus systems with imperfectly repairable components," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 58-66.
    9. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2015. "Optimal backup frequency in system with random repair time," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 12-22.
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