IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v134y2015icp230-238.html
   My bibliography  Save this article

An optimal age-based group maintenance policy for multi-unit degrading systems

Author

Listed:
  • Shafiee, Mahmood
  • Finkelstein, Maxim

Abstract

In order to share maintenance set-up costs and reduce system breakdown, the group maintenance policies are widely used for complex multi-unit systems. In this paper, an optimal age-based group maintenance policy is proposed for a multi-unit series system whose components are subject to different gradual degradation phenomena. When the degradation level of a component reaches a given critical size, it is replaced by a new one and the other components undergo a preventive maintenance (PM) action; otherwise, a planned group PM is performed for the whole system at operational age T>0. The problem is to determine an optimal group maintenance time T⠎ such that the system’s average long-run maintenance cost per unit time is minimized. The explicit expression of the objective function is derived and sufficient conditions for existence and uniqueness of the optimal solution are obtained. Finally, the proposed maintenance policy is applied to a group of wind turbine bearings and the results are compared with the case without planned maintenance (i.e., reactive response) and with an individual age-based maintenance policy.

Suggested Citation

  • Shafiee, Mahmood & Finkelstein, Maxim, 2015. "An optimal age-based group maintenance policy for multi-unit degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 230-238.
    • Handle: RePEc:eee:reensy:v:134:y:2015:i:c:p:230-238
    DOI: 10.1016/j.ress.2014.09.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832014002324
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2014.09.016?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. Khac Tuan Huynh & Inma T. Castro & Anne Barros & Christophe Bérenguer, 2012. "Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks," Post-Print hal-00790729, HAL.
    2. Toshio Nakagawa, 2007. "Shock and Damage Models in Reliability Theory," Springer Series in Reliability Engineering, Springer, number 978-1-84628-442-7, January.
    3. Robin P. Nicolai & Rommert Dekker, 2008. "Optimal Maintenance of Multi-component Systems: A Review," Springer Series in Reliability Engineering, in: Complex System Maintenance Handbook, chapter 11, pages 263-286, Springer.
    4. van der Weide, J.A.M. & Pandey, M.D. & van Noortwijk, J.M., 2010. "Discounted cost model for condition-based maintenance optimization," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 236-246.
    5. M D Pandey & T Cheng & J A M van der Weide, 2011. "Finite-time maintenance cost analysis of engineering systems affected by stochastic degradation," Journal of Risk and Reliability, , vol. 225(2), pages 241-250, June.
    6. Khac Tuan Huynh & Anne Barros & Christophe Bérenguer & Inma T. Castro, 2011. "A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events," Post-Print hal-00790728, HAL.
    7. Huynh, K.T. & Barros, A. & Bérenguer, C. & Castro, I.T., 2011. "A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 497-508.
    8. Mahmood Shafiee & Fateme Dinmohammadi, 2014. "An FMEA-Based Risk Assessment Approach for Wind Turbine Systems: A Comparative Study of Onshore and Offshore," Energies, MDPI, vol. 7(2), pages 1-24, February.
    9. Huynh, K.T. & Castro, I.T. & Barros, A. & Bérenguer, C., 2012. "Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks," European Journal of Operational Research, Elsevier, vol. 218(1), pages 140-151.
    10. Aven, Terje & Castro, I.T., 2008. "A minimal repair replacement model with two types of failure and a safety constraint," European Journal of Operational Research, Elsevier, vol. 188(2), pages 506-515, July.
    11. Shafiee, Mahmood & Chukova, Stefanka, 2013. "Maintenance models in warranty: A literature review," European Journal of Operational Research, Elsevier, vol. 229(3), pages 561-572.
    12. Hongzhou Wang & Hoang Pham, 2006. "Reliability and Optimal Maintenance," Springer Series in Reliability Engineering, Springer, number 978-1-84628-325-3, January.
    13. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, January.
    14. J. H. Park & S. C. Lee & J. W. Hong & C. H. Lie, 2009. "An Optimal Block Preventive Maintenance Policy For A Multi-Unit System Considering Imperfect Maintenance," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(06), pages 831-847.
    15. Maxim Finkelstein & Ji Hwan Cha, 2013. "Burn-in for Heterogeneous Populations," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 261-312, Springer.
    16. Alaa H. Elwany & Nagi Z. Gebraeel & Lisa M. Maillart, 2011. "Structured Replacement Policies for Components with Complex Degradation Processes and Dedicated Sensors," Operations Research, INFORMS, vol. 59(3), pages 684-695, June.
    17. I. T. Castro, 2013. "An Age-Based Maintenance Strategy For A Degradation-Threshold-Shock-Model For A System Subjected To Multiple Defects," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-14.
    18. Zafar Hameed & Jørn Vatn, 2012. "Role of grouping in the development of an overall maintenance optimization framework for offshore wind turbines," Journal of Risk and Reliability, , vol. 226(6), pages 584-601, December.
    19. Do Van, Phuc & Barros, Anne & Bérenguer, Christophe & Bouvard, Keomany & Brissaud, Florent, 2013. "Dynamic grouping maintenance with time limited opportunities," Reliability Engineering and System Safety, Elsevier, vol. 120(C), pages 51-59.
    20. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
    21. Van Horenbeek, Adriaan & Pintelon, Liliane, 2013. "A dynamic predictive maintenance policy for complex multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 120(C), pages 39-50.
    22. Hong, H.P. & Zhou, W. & Zhang, S. & Ye, W., 2014. "Optimal condition-based maintenance decisions for systems with dependent stochastic degradation of components," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 276-288.
    23. Chien-Kuo Sung & Shey-Huei Sheu & Tsung-Shin Hsu & Yan-Chun Chen, 2013. "Extended optimal replacement policy for a two-unit system with failure rate interaction and external shocks," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(5), pages 877-888.
    24. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
    25. Maaroufi, Ghofrane & Chelbi, Anis & Rezg, Nidhal, 2013. "Optimal selective renewal policy for systems subject to propagated failures with global effect and failure isolation phenomena," Reliability Engineering and System Safety, Elsevier, vol. 114(C), pages 61-70.
    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. Zhou, Xiaojun & Shi, Kailong, 2019. "Capacity failure rate based opportunistic maintenance modeling for series-parallel multi-station manufacturing systems," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 46-53.
    2. Özgür-Ünlüakın, Demet & Türkali, Busenur, 2021. "Evaluation of proactive maintenance policies on a stochastically dependent hidden multi-component system using DBNs," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    3. Shafiee, Mahmood & Finkelstein, Maxim & Bérenguer, Christophe, 2015. "An opportunistic condition-based maintenance policy for offshore wind turbine blades subjected to degradation and environmental shocks," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 463-471.
    4. Gia-Shie Liu, 2019. "A Group Replacement Decision Support System Based on Internet of Things," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
    5. Wu, Tianyi & Yang, Li & Ma, Xiaobing & Zhang, Zihan & Zhao, Yu, 2020. "Dynamic maintenance strategy with iteratively updated group information," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    6. McMorland, Jade & Flannigan, Callum & Carroll, James & Collu, Maurizio & McMillan, David & Leithead, William & Coraddu, Andrea, 2022. "A review of operations and maintenance modelling with considerations for novel wind turbine concepts," Renewable and Sustainable Energy Reviews, Elsevier, vol. 165(C).
    7. Tobi Elusakin & Mahmood Shafiee & Tosin Adedipe & Fateme Dinmohammadi, 2021. "A Stochastic Petri Net Model for O&M Planning of Floating Offshore Wind Turbines," Energies, MDPI, vol. 14(4), pages 1-18, February.
    8. Duan, Chaoqun & Makis, Viliam & Deng, Chao, 2020. "A two-level Bayesian early fault detection for mechanical equipment subject to dependent failure modes," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    9. Aizpurua, J.I. & Catterson, V.M. & Papadopoulos, Y. & Chiacchio, F. & D'Urso, D., 2017. "Supporting group maintenance through prognostics-enhanced dynamic dependability prediction," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 171-188.
    10. Li Yang & Yu Zhao & Xiaobing Ma & Qingan Qiu, 2018. "An optimal inspection and replacement policy for a two-unit system," Journal of Risk and Reliability, , vol. 232(6), pages 766-776, December.
    11. Shafiee, Mahmood & Sørensen, John Dalsgaard, 2019. "Maintenance optimization and inspection planning of wind energy assets: Models, methods and strategies," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    12. Thomas Michael Welte & Iver Bakken Sperstad & Espen Høegh Sørum & Magne Lorentzen Kolstad, 2017. "Integration of Degradation Processes in a Strategic Offshore Wind Farm O&M Simulation Model," Energies, MDPI, vol. 10(7), pages 1-18, July.
    13. Mikhail, Mina & Ouali, Mohamed-Salah & Yacout, Soumaya, 2024. "A data-driven methodology with a nonparametric reliability method for optimal condition-based maintenance strategies," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    14. Zhang, Nan & Cai, Kaiquan & Deng, Yingjun & Zhang, Jun, 2024. "Joint optimization of condition-based maintenance and condition-based production of a single equipment considering random yield and maintenance delay," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    15. Yang, Li & Zhao, Yu & Peng, Rui & Ma, Xiaobing, 2018. "Hybrid preventive maintenance of competing failures under random environment," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 130-140.
    16. Mahmood Shafiee & Ashraf Labib & Jhareswar Maiti & Andrew Starr, 2019. "Maintenance strategy selection for multi-component systems using a combined analytic network process and cost-risk criticality model," Journal of Risk and Reliability, , vol. 233(2), pages 89-104, April.
    17. Do, Phuc & Vu, Hai Canh & Barros, Anne & Bérenguer, Christophe, 2015. "Maintenance grouping for multi-component systems with availability constraints and limited maintenance teams," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 56-67.
    18. Xian Zhao & Rong Li & Yu Fan & Qingan Qiu, 2022. "Reliability modeling for multi-state systems with a protective device considering multiple triggering mechanism," Journal of Risk and Reliability, , vol. 236(1), pages 173-193, February.
    19. Zhao, Xufeng & Al-Khalifa, Khalifa N. & Magid Hamouda, Abdel & Nakagawa, Toshio, 2017. "Age replacement models: A summary with new perspectives and methods," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 95-105.
    20. Tazi, Nacef & Châtelet, Eric & Bouzidi, Youcef, 2018. "How combined performance and propagation of failure dependencies affect the reliability of a MSS," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 531-541.
    21. Shafiee, Mahmood, 2015. "Maintenance logistics organization for offshore wind energy: Current progress and future perspectives," Renewable Energy, Elsevier, vol. 77(C), pages 182-193.
    22. 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.
    23. Mahmood Shafiee & Maxim Finkelstein, 2015. "A proactive group maintenance policy for continuously monitored deteriorating systems: Application to offshore wind turbines," Journal of Risk and Reliability, , vol. 229(5), pages 373-384, October.
    24. 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.
    25. Zhao, Yixin & Cozzani, Valerio & Sun, Tianqi & Vatn, Jørn & Liu, Yiliu, 2023. "Condition-based maintenance for a multi-component system subject to heterogeneous failure dependences," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

    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. Mahmood Shafiee & Maxim Finkelstein, 2015. "A proactive group maintenance policy for continuously monitored deteriorating systems: Application to offshore wind turbines," Journal of Risk and Reliability, , vol. 229(5), pages 373-384, October.
    2. Shafiee, Mahmood & Finkelstein, Maxim & Bérenguer, Christophe, 2015. "An opportunistic condition-based maintenance policy for offshore wind turbine blades subjected to degradation and environmental shocks," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 463-471.
    3. Caballé, N.C. & Castro, I.T. & Pérez, C.J. & Lanza-Gutiérrez, J.M., 2015. "A condition-based maintenance of a dependent degradation-threshold-shock model in a system with multiple degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 98-109.
    4. Alaswad, Suzan & Xiang, Yisha, 2017. "A review on condition-based maintenance optimization models for stochastically deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 54-63.
    5. Ji Hwan Cha & Maxim Finkelstein, 2019. "Optimal preventive maintenance for systems having a continuous output and operating in a random environment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 327-350, July.
    6. Ji Hwan Cha & Maxim Finkelstein & Gregory Levitin, 2017. "Bivariate preventive maintenance for repairable systems subject to random shocks," Journal of Risk and Reliability, , vol. 231(6), pages 643-653, December.
    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. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2018. "Bivariate preventive maintenance of systems with lifetimes dependent on a random shock process," European Journal of Operational Research, Elsevier, vol. 266(1), pages 122-134.
    9. Ji Hwan Cha & Maxim Finkelstein, 2019. "On some characteristics of quality for systems operating in a random environment," Journal of Risk and Reliability, , vol. 233(2), pages 257-267, April.
    10. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    11. Hai-Kun Wang & Yan-Feng Li & Yu Liu & Yuan-Jian Yang & Hong-Zhong Huang, 2015. "Remaining useful life estimation under degradation and shock damage," Journal of Risk and Reliability, , vol. 229(3), pages 200-208, June.
    12. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.
    13. Ji Hwan Cha & Maxim Finkelstein, 2018. "On a New Shot Noise Process and the Induced Survival Model," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 897-917, September.
    14. Levitin, Gregory & Finkelstein, Maxim, 2019. "Optimal loading of elements in series systems exposed to external shocks," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    15. N. C. Caballé & I. T. Castro, 2019. "Assessment of the maintenance cost and analysis of availability measures in a finite life cycle for a system subject to competing failures," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 255-290, March.
    16. de Jonge, Bram, 2019. "Discretizing continuous-time continuous-state deterioration processes, with an application to condition-based maintenance optimization," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 1-5.
    17. Zhang, Jian & Huang, Xiaoyan & Fang, Youtong & Zhou, Jing & Zhang, He & Li, Jing, 2016. "Optimal inspection-based preventive maintenance policy for three-state mechanical components under competing failure modes," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 95-103.
    18. Hazra, Nil Kamal & Finkelstein, Maxim & Cha, Ji Hwan, 2022. "On a hazard (failure) rate process with delays after shocks," Statistics & Probability Letters, Elsevier, vol. 181(C).
    19. Cha, Ji Hwan & Finkelstein, Maxim, 2018. "On information-based residual lifetime in survival models with delayed failures," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 209-216.
    20. Huynh, K.T. & Grall, A. & Bérenguer, C., 2017. "Assessment of diagnostic and prognostic condition indices for efficient and robust maintenance decision-making of systems subject to stress corrosion cracking," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 237-254.

    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:reensy:v:134:y:2015:i:c:p:230-238. 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: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.