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An extended optimal replacement model for a deteriorating system with inspections

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  • Sheu, Shey-Huei
  • Tsai, Hsin-Nan
  • Wang, Fu-Kwun
  • Zhang, Zhe George

Abstract

This study considers a generalized replacement model for a deteriorating system in which failures can only be detected by inspection. The system is assumed to have two types of failures and is replaced at the occurrence of the Nth type I failure (minor failure), or the first type II failure (catastrophic failure), or at working age T, whichever occurs first. The probability of a type I or type II failure depends on the number of type I failures since the previous replacement. Such a system can be repaired after a type I failure, but is deteriorating stochastically. That is, the operating intervals are decreasing stochastically, whereas the durations of the repairs are increasing stochastically. Based on these assumptions, we determine the expected net cost rate and discuss various special cases of the model. Finally, we develop a computational algorithm for finding the optimal policy and present a numerical example to show the properties of the proposed model.

Suggested Citation

  • Sheu, Shey-Huei & Tsai, Hsin-Nan & Wang, Fu-Kwun & Zhang, Zhe George, 2015. "An extended optimal replacement model for a deteriorating system with inspections," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 33-49.
    • Handle: RePEc:eee:reensy:v:139:y:2015:i:c:p:33-49
    DOI: 10.1016/j.ress.2015.01.014
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    References listed on IDEAS

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    1. Flage, Roger, 2014. "A delay time model with imperfect and failure-inducing inspections," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 1-12.
    2. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    3. Shey-Huei Sheu & Griffith, William S. & Toshio Nakagawa, 1995. "Extended optimal replacement model with random minimal repair costs," European Journal of Operational Research, Elsevier, vol. 85(3), pages 636-649, September.
    4. Xia, Tangbin & Xi, Lifeng & Zhou, Xiaojun & Lee, Jay, 2012. "Dynamic maintenance decision-making for series–parallel manufacturing system based on MAM–MTW methodology," European Journal of Operational Research, Elsevier, vol. 221(1), pages 231-240.
    5. Wang, Wenbin, 2009. "An inspection model for a process with two types of inspections and repairs," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 526-533.
    6. Toshio Nakagawa, 2014. "Random Inspection Policies," Springer Series in Reliability Engineering, in: Random Maintenance Policies, edition 127, chapter 0, pages 87-114, Springer.
    7. G.Q. Cheng & L. Li, 2012. "A geometric process repair model with inspections and its optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(9), pages 1650-1655.
    8. H. W. Block & W. S. Borges & T. H. Savits, 1988. "A general age replacement model with minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 365-372, October.
    9. Philip J. Boland & Frank Proschan, 1982. "Periodic Replacement with Increasing Minimal Repair Costs at Failure," Operations Research, INFORMS, vol. 30(6), pages 1183-1189, December.
    10. Nakagawa, T. & Mizutani, S. & Chen, M., 2010. "A summary of periodic and random inspection policies," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 906-911.
    11. Sheu, Shey-Huei, 1999. "Extended optimal replacement model for deteriorating systems," European Journal of Operational Research, Elsevier, vol. 112(3), pages 503-516, February.
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    Cited by:

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    4. Badía, F.G. & Berrade, M.D. & Cha, Ji Hwan & Lee, Hyunju, 2018. "Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 362-372.
    5. Yang, Li & Ye, Zhi-sheng & Lee, Chi-Guhn & Yang, Su-fen & Peng, Rui, 2019. "A two-phase preventive maintenance policy considering imperfect repair and postponed replacement," European Journal of Operational Research, Elsevier, vol. 274(3), pages 966-977.
    6. Qiu, Qingan & Cui, Lirong & Gao, Hongda & Yi, He, 2018. "Optimal allocation of units in sequential probability series systems," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 351-363.
    7. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    8. Yang, Li & Ma, Xiaobing & Peng, Rui & Zhai, Qingqing & Zhao, Yu, 2017. "A preventive maintenance policy based on dependent two-stage deterioration and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 201-211.
    9. Badía, F.G. & Berrade, M.D. & Lee, Hyunju, 2020. "An study of cost effective maintenance policies: Age replacement versus replacement after N minimal repairs," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

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