IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v108y2012icp65-76.html
   My bibliography  Save this article

The probability distribution of maintenance cost of a system affected by the gamma process of degradation: Finite time solution

Author

Listed:
  • Cheng, Tianjin
  • Pandey, Mahesh D.
  • van der Weide, J.A.M.

Abstract

The stochastic gamma process has been widely used to model uncertain degradation in engineering systems and structures. The optimization of the condition-based maintenance (CBM) policy is typically based on the minimization of the asymptotic cost rate. In the financial planning of a maintenance program, however, a more accurate prediction interval for the cost is needed for prudent decision making. The prediction interval cannot be estimated unless the probability distribution of cost is known. In this context, the asymptotic cost rate has a limited utility.

Suggested Citation

  • Cheng, Tianjin & Pandey, Mahesh D. & van der Weide, J.A.M., 2012. "The probability distribution of maintenance cost of a system affected by the gamma process of degradation: Finite time solution," Reliability Engineering and System Safety, Elsevier, vol. 108(C), pages 65-76.
    • Handle: RePEc:eee:reensy:v:108:y:2012:i:c:p:65-76
    DOI: 10.1016/j.ress.2012.06.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S095183201200110X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2012.06.005?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. Nicolai, Robin P. & Dekker, Rommert & van Noortwijk, Jan M., 2007. "A comparison of models for measurable deterioration: An application to coatings on steel structures," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1635-1650.
    2. Kallen, M.J. & van Noortwijk, J.M., 2005. "Optimal maintenance decisions under imperfect inspection," Reliability Engineering and System Safety, Elsevier, vol. 90(2), pages 177-185.
    3. 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.
    4. Nakagawa, T. & Mizutani, S., 2009. "A summary of maintenance policies for a finite interval," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 89-96.
    5. 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.
    6. van Noortwijk, J.M. & van der Weide, J.A.M. & Kallen, M.J. & Pandey, M.D., 2007. "Gamma processes and peaks-over-threshold distributions for time-dependent reliability," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1651-1658.
    7. Jiang, R., 2009. "An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1245-1250.
    8. C Meier-Hirmer & G Riboulet & F Sourget & M Roussignol, 2009. "Maintenance optimization for a system with a gamma deterioration process and intervention delay: Application to track maintenance," Journal of Risk and Reliability, , vol. 223(3), pages 189-198, September.
    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. Zhang, Nailong & Si, Wujun, 2020. "Deep reinforcement learning for condition-based maintenance planning of multi-component systems under dependent competing risks," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    2. Shi, Guannan & Zhang, Xiaohong & Zeng, Jianchao & Liao, Haitao & Shi, Hui & Niu, Huifang & Wang, Jinhe, 2024. "A chance-constrained net revenue model for online dynamic predictive maintenance decision-making," Reliability Engineering and System Safety, Elsevier, vol. 249(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. Li, Yaohan & Dong, You & Guo, Hongyuan, 2023. "Copula-based multivariate renewal model for life-cycle analysis of civil infrastructure considering multiple dependent deterioration processes," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    5. 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.
    6. Pedersen, Tom Ivar & Vatn, Jørn, 2022. "Optimizing a condition-based maintenance policy by taking the preferences of a risk-averse decision maker into account," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    7. Liu, Bin & Xu, Zhengguo & Xie, Min & Kuo, Way, 2014. "A value-based preventive maintenance policy for multi-component system with continuously degrading components," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 83-89.
    8. Yi Yang & John Dalsgaard Sørensen, 2019. "Cost-Optimal Maintenance Planning for Defects on Wind Turbine Blades," Energies, MDPI, vol. 12(6), pages 1-16, March.
    9. 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.
    10. 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.
    11. Mahesh D Pandey & Tianjin Cheng & JAM Van der Weide, 2016. "Higher moments and probability distribution of maintenance cost in the delay time model," Journal of Risk and Reliability, , vol. 230(4), pages 354-363, August.
    12. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    13. Zhao, Yan-Gang & Zhang, Xuan-Yi & Lu, Zhao-Hui, 2018. "A flexible distribution and its application in reliability engineering," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 1-12.

    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. 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.
    2. 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.
    3. 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.
    4. A Ponchet & M Fouladirad & A Grall, 2011. "Maintenance policy on a finite time span for a gradually deteriorating system with imperfect improvements," Journal of Risk and Reliability, , vol. 225(2), pages 105-116, June.
    5. Ponchet, Amélie & Fouladirad, Mitra & Grall, Antoine, 2010. "Assessment of a maintenance model for a multi-deteriorating mode system," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1244-1254.
    6. Cárdenas-Gallo, Iván & Sarmiento, Carlos A. & Morales, Gilberto A. & Bolivar, Manuel A. & Akhavan-Tabatabaei, Raha, 2017. "An ensemble classifier to predict track geometry degradation," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 53-60.
    7. Wang, Changxi & Elsayed, Elsayed A., 2020. "Stochastic modeling of corrosion growth," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    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. Guida, M. & Postiglione, F. & Pulcini, G., 2012. "A time-discrete extended gamma process for time-dependent degradation phenomena," Reliability Engineering and System Safety, Elsevier, vol. 105(C), pages 73-79.
    10. Kuniewski, Sebastian P. & van der Weide, Johannes A.M. & van Noortwijk, Jan M., 2009. "Sampling inspection for the evaluation of time-dependent reliability of deteriorating systems under imperfect defect detection," Reliability Engineering and System Safety, Elsevier, vol. 94(9), pages 1480-1490.
    11. Nicolai, R.P. & Frenk, J.B.G. & Dekker, R., 2007. "Modelling and Optimizing Imperfect Maintenance of Coatings on Steel Structures," ERIM Report Series Research in Management ERS-2007-043-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    12. Liu, Xingheng & Matias, José & Jäschke, Johannes & Vatn, Jørn, 2022. "Gibbs sampler for noisy Transformed Gamma process: Inference and remaining useful life estimation," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    13. Finkelstein, Maxim & Ludick, Zani, 2014. "On some steady-state characteristics of systems with gradual repair," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 17-23.
    14. Guo, Chiming & Wang, Wenbin & Guo, Bo & Si, Xiaosheng, 2013. "A maintenance optimization model for mission-oriented systems based on Wiener degradation," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 183-194.
    15. Esposito, Nicola & Mele, Agostino & Castanier, Bruno & GIORGIO, Massimiliano, 2023. "A hybrid maintenance policy for a deteriorating unit in the presence of three forms of variability," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    16. C Meier-Hirmer & G Riboulet & F Sourget & M Roussignol, 2009. "Maintenance optimization for a system with a gamma deterioration process and intervention delay: Application to track maintenance," Journal of Risk and Reliability, , vol. 223(3), pages 189-198, September.
    17. Hazra, Indranil & Pandey, Mahesh D. & Manzana, Noldainerick, 2020. "Approximate Bayesian computation (ABC) method for estimating parameters of the gamma process using noisy data," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    18. 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.
    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. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.

    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:108:y:2012:i:c:p:65-76. 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.