IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v266y2018i3p963-975.html
   My bibliography  Save this article

Sensitivity of optimal replacement policies to lifetime parameter estimates

Author

Listed:
  • Fouladirad, Mitra
  • Paroissin, Christian
  • Grall, Antoine

Abstract

This paper analyzes three time-based replacement policies when the parameters of the time-to-failure distribution are unknown. Under the hypothesis of a large sample data, the unknown parameters are estimated via maximum likelihood method. The uncertainty around the point estimates impacts the maintenance decision rules. Based on the asymptotic normality of the parameter estimators and delta-method, the asymptotic distribution of the optimal decision parameter and the average cost is derived. This distribution permits to measure the uncertainty around the optimal maintenance decision rule induced by the point estimates. The sensitivity analysis of the replacement policies to the maintenance unit costs and lifetime distribution parameters is carried out. Application to two time-to-failure distributions is provided.

Suggested Citation

  • Fouladirad, Mitra & Paroissin, Christian & Grall, Antoine, 2018. "Sensitivity of optimal replacement policies to lifetime parameter estimates," European Journal of Operational Research, Elsevier, vol. 266(3), pages 963-975.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:3:p:963-975
    DOI: 10.1016/j.ejor.2017.10.055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717309682
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.10.055?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kijima, Masaaki & Morimura, Hidenori & Suzuki, Yasusuke, 1988. "Periodical replacement problem without assuming minimal repair," European Journal of Operational Research, Elsevier, vol. 37(2), pages 194-203, November.
    2. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    3. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    4. Bedford, Tim & Wilson, Kevin J. & Daneshkhah, Alireza, 2014. "Assessing parameter uncertainty on coupled models using minimum information methods," Reliability Engineering and System Safety, Elsevier, vol. 125(C), pages 3-12.
    5. de Jonge, Bram & Klingenberg, Warse & Teunter, Ruud & Tinga, Tiedo, 2015. "Optimum maintenance strategy under uncertainty in the lifetime distribution," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 59-67.
    6. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    7. Silver, Edward A. & Fiechter, Claude-Nicolas, 1992. "A simple case of preventive maintenance decision-making with limited historical data," International Journal of Production Economics, Elsevier, vol. 27(3), pages 241-250, October.
    8. de Jonge, Bram & Dijkstra, Arjan S. & Romeijnders, Ward, 2015. "Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 15-21.
    9. Silver, Edward A. & Fiechter, Claude-Nicolas, 1995. "Preventive maintenance with limited historical data," European Journal of Operational Research, Elsevier, vol. 82(1), pages 125-144, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimization of cyclic preventive replacement in homogeneous warm-standby system with reusable elements exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    2. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2022. "Optimal preventive switching of components in degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    3. 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.
    4. Eryilmaz, Serkan, 2021. "Revisiting discrete time age replacement policy for phase-type lifetime distributions," European Journal of Operational Research, Elsevier, vol. 295(2), pages 699-704.
    5. Salem, Marwa Belhaj & Fouladirad, Mitra & Deloux, Estelle, 2022. "Variance Gamma process as degradation model for prognosis and imperfect maintenance of centrifugal pumps," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    6. Zhu, Zhicheng & Xiang, Yisha & Zhao, Ming & Shi, Yue, 2023. "Data-driven remanufacturing planning with parameter uncertainty," European Journal of Operational Research, Elsevier, vol. 309(1), pages 102-116.
    7. Alotaibi, Naif M. & Scarf, Philip & Cavalcante, Cristiano A.V. & Lopes, Rodrigo S. & de Oliveira e Silva, André Luiz & Rodrigues, Augusto J.S. & Alyami, Salem A., 2023. "Modified-opportunistic inspection and the case of remote, groundwater well-heads," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    8. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Optimal preventive replacement policy for homogeneous cold standby systems with reusable elements," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    9. Chatenet, Q. & Remy, E. & Gagnon, M. & Fouladirad, M. & Tahan, A.S., 2021. "Modeling cavitation erosion using non-homogeneous gamma process," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    10. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    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. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimal shock-driven switching strategies with elements reuse in heterogeneous warm-standby systems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    13. Vanderschueren, Toon & Boute, Robert & Verdonck, Tim & Baesens, Bart & Verbeke, Wouter, 2023. "Optimizing the preventive maintenance frequency with causal machine learning," International Journal of Production Economics, Elsevier, vol. 258(C).
    14. Sarkhosh S Chaharborj & Norsarahaida Amin, 2020. "Controlling the pressure of hydrogen-natural gas mixture in an inclined pipeline," PLOS ONE, Public Library of Science, vol. 15(2), pages 1-19, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. de Jonge, Bram & Dijkstra, Arjan S. & Romeijnders, Ward, 2015. "Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 15-21.
    2. Briš, Radim & Byczanski, Petr & Goňo, Radomír & Rusek, Stanislav, 2017. "Discrete maintenance optimization of complex multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 80-89.
    3. de Jonge, Bram & Klingenberg, Warse & Teunter, Ruud & Tinga, Tiedo, 2015. "Optimum maintenance strategy under uncertainty in the lifetime distribution," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 59-67.
    4. de Jonge, Bram & Teunter, Ruud & Tinga, Tiedo, 2017. "The influence of practical factors on the benefits of condition-based maintenance over time-based maintenance," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 21-30.
    5. Sidibe, I.B. & Khatab, A. & Diallo, C. & Kassambara, A., 2017. "Preventive maintenance optimization for a stochastically degrading system with a random initial age," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 255-263.
    6. Toledo, Maria Luíza Guerra de & Freitas, Marta A. & Colosimo, Enrico A. & Gilardoni, Gustavo L., 2015. "ARA and ARI imperfect repair models: Estimation, goodness-of-fit and reliability prediction," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 107-115.
    7. Gilardoni, Gustavo L. & de Toledo, Maria Luiza Guerra & Freitas, Marta A. & Colosimo, Enrico A., 2016. "Dynamics of an optimal maintenance policy for imperfect repair models," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1104-1112.
    8. Vanderschueren, Toon & Boute, Robert & Verdonck, Tim & Baesens, Bart & Verbeke, Wouter, 2023. "Optimizing the preventive maintenance frequency with causal machine learning," International Journal of Production Economics, Elsevier, vol. 258(C).
    9. de Jonge, Bram & Jakobsons, Edgars, 2018. "Optimizing block-based maintenance under random machine usage," European Journal of Operational Research, Elsevier, vol. 265(2), pages 703-709.
    10. Truong Ba, H. & Cholette, M.E. & Borghesani, P. & Zhou, Y. & Ma, L., 2017. "Opportunistic maintenance considering non-homogenous opportunity arrivals and stochastic opportunity durations," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 151-161.
    11. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    12. 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.
    13. Hashemi, M. & Asadi, M. & Zarezadeh, S., 2020. "Optimal maintenance policies for coherent systems with multi-type components," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    14. 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.
    15. Wu, Shaomin & Scarf, Philip, 2015. "Decline and repair, and covariate effects," European Journal of Operational Research, Elsevier, vol. 244(1), pages 219-226.
    16. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2023. "Improving classical optimal age-replacement policies for degrading items," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    17. Guo R. & Ascher H. & Love E., 2001. "Towards Practical and Synthetical Modelling of Repairable Systems," Stochastics and Quality Control, De Gruyter, vol. 16(1), pages 147-182, January.
    18. Ji Hwan Cha & Maxim Finkelstein, 2020. "On optimal life extension for degrading systems," Journal of Risk and Reliability, , vol. 234(3), pages 487-495, June.
    19. Ammar Y. Alqahtani & Surendra M. Gupta, 2017. "One-Dimensional Renewable Warranty Management within Sustainable Supply Chain," Resources, MDPI, vol. 6(2), pages 1-26, April.
    20. Belyi, Dmitriy & Popova, Elmira & Morton, David P. & Damien, Paul, 2017. "Bayesian failure-rate modeling and preventive maintenance optimization," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1085-1093.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:266:y:2018:i:3:p:963-975. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.