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An Adaptive Bayesian Replacement Policy with Minimal Repair

Author

Listed:
  • Savaş Dayanik

    (Department of IEOR, Columbia University, New York, New York 10027)

  • Ülkü Gürler

    (Faculty of Engineering, Bilkent University, 06533 Bilkent, Ankara, Turkey)

Abstract

In this study, an adaptive Bayesian decision model is developed to determine the optimal replacement age for the systems maintained according to a general age-replacement policy. It is assumed that when a failure occurs, it is either critical with probability p or noncritical with probability 1 -- p , independently. A maintenance policy is considered where the noncritical failures are corrected with minimal repair and the system is replaced either at the first critical failure or at age (tau), whichever occurs first. The aim is to find the optimal value of (tau) that minimizes the expected cost per unit time. Two adaptive Bayesian procedures that utilize different levels of information are proposed for sequentially updating the optimal replacement times. Posterior density/mass functions of the related variables are derived when the time to failure for the system can be expressed as a Weibull random variable. Some simulation results are also presented for illustration purposes.

Suggested Citation

  • Savaş Dayanik & Ülkü Gürler, 2002. "An Adaptive Bayesian Replacement Policy with Minimal Repair," Operations Research, INFORMS, vol. 50(3), pages 552-558, June.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:3:p:552-558
    DOI: 10.1287/opre.50.3.552.7750
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    References listed on IDEAS

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    1. Frank Beichelt, 1993. "A unifying treatment of replacement policies with minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 51-67, February.
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    Citations

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    Cited by:

    1. Mamabolo R. M. & Beichelt F. E., 2004. "Maintenance Policies with Minimal Repair," Stochastics and Quality Control, De Gruyter, vol. 19(2), pages 143-166, January.
    2. Andrés Christen, J. & Ruggeri, Fabrizio & Villa, Enrique, 2011. "Utility based maintenance analysis using a Random Sign censoring model," Reliability Engineering and System Safety, Elsevier, vol. 96(3), pages 425-431.
    3. Zhao, Xufeng & Liu, Hu-Chen & Nakagawa, Toshio, 2015. "Where does “whichever occurs first†hold for preventive maintenance modelings?," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 203-211.
    4. Makis, Viliam, 2009. "Multivariate Bayesian process control for a finite production run," European Journal of Operational Research, Elsevier, vol. 194(3), pages 795-806, May.
    5. Ludvík Friebel & Jana Friebelová, 2012. "Stochastic analysis of maintenance process costs in the IT industry: a case study," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(3), pages 393-408, September.
    6. Insua, David Rios & Ruggeri, Fabrizio & Soyer, Refik & Wilson, Simon, 2020. "Advances in Bayesian decision making in reliability," European Journal of Operational Research, Elsevier, vol. 282(1), pages 1-18.
    7. Hu, Jiawen & Chen, Piao, 2020. "Predictive maintenance of systems subject to hard failure based on proportional hazards model," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    8. Yeu‐Shiang Huang & Chi‐Chang Hung & Chih‐Chiang Fang, 2008. "Bayesian enhanced decision making for deteriorating repairable systems with preventive maintenance," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(2), pages 105-115, March.
    9. Dursun, İpek & Akçay, Alp & van Houtum, Geert-Jan, 2022. "Age-based maintenance under population heterogeneity: Optimal exploration and exploitation," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1007-1020.
    10. Michael Jong Kim, 2020. "Variance Regularization in Sequential Bayesian Optimization," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 966-992, August.
    11. Dursun, İpek & Akçay, Alp & van Houtum, Geert-Jan, 2022. "Data pooling for multiple single-component systems under population heterogeneity," International Journal of Production Economics, Elsevier, vol. 250(C).
    12. Zu‐Liang Lin & Yeu‐Shiang Huang, 2010. "Nonperiodic preventive maintenance for repairable systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(7), pages 615-625, October.
    13. Michael Jong Kim & Viliam Makis, 2013. "Joint Optimization of Sampling and Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 61(3), pages 777-790, June.
    14. Flage, Roger & Coit, David W. & Luxhøj, James T. & Aven, Terje, 2012. "Safety constraints applied to an adaptive Bayesian condition-based maintenance optimization model," Reliability Engineering and System Safety, Elsevier, vol. 102(C), pages 16-26.
    15. Vinayak Deshpande & Ananth V. Iyer & Richard Cho, 2006. "Efficient Supply Chain Management at the U.S. Coast Guard Using Part-Age Dependent Supply Replenishment Policies," Operations Research, INFORMS, vol. 54(6), pages 1028-1040, December.
    16. Michael Jong Kim, 2016. "Robust Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 64(4), pages 999-1014, August.

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