IDEAS home Printed from
   My bibliography  Save this article

A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution


  • Si, Xiao-Sheng
  • Wang, Wenbin
  • Chen, Mao-Yin
  • Hu, Chang-Hua
  • Zhou, Dong-Hua


Remaining useful life (RUL) estimation is regarded as one of the most central components in prognostics and health management (PHM). Accurate RUL estimation can enable failure prevention in a more controllable manner in that effective maintenance can be executed in appropriate time to correct impending faults. In this paper we consider the problem of estimating the RUL from observed degradation data for a general system. A degradation path-dependent approach for RUL estimation is presented through the combination of Bayesian updating and expectation maximization (EM) algorithm. The use of both Bayesian updating and EM algorithm to update the model parameters and RUL distribution at the time obtaining a newly observed data is a novel contribution of this paper, which makes the estimated RUL depend on the observed degradation data history. As two specific cases, a linear degradation model and an exponential-based degradation model are considered to illustrate the implementation of our presented approach. A major contribution under these two special cases is that our approach can obtain an exact and closed-form RUL distribution respectively, and the moment of the obtained RUL distribution from our presented approach exists. This contrasts sharply with the approximated results obtained in the literature for the same cases. To our knowledge, the RUL estimation approach presented in this paper for the two special cases is the only one that can provide an exact and closed-form RUL distribution utilizing the monitoring history. Finally, numerical examples for RUL estimation and a practical case study for condition-based replacement decision making with comparison to a previously reported approach are provided to substantiate the superiority of the proposed model.

Suggested Citation

  • Si, Xiao-Sheng & Wang, Wenbin & Chen, Mao-Yin & Hu, Chang-Hua & Zhou, Dong-Hua, 2013. "A degradation path-dependent approach for remaining useful life estimation with an exact and closed-form solution," European Journal of Operational Research, Elsevier, vol. 226(1), pages 53-66.
  • Handle: RePEc:eee:ejores:v:226:y:2013:i:1:p:53-66
    DOI: 10.1016/j.ejor.2012.10.030

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

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

    References listed on IDEAS

    1. Carr, Matthew J. & Wang, Wenbin, 2011. "An approximate algorithm for prognostic modelling using condition monitoring information," European Journal of Operational Research, Elsevier, vol. 211(1), pages 90-96, May.
    2. repec:eee:reensy:v:94:y:2009:i:2:p:509-519 is not listed on IDEAS
    3. Wang, W. & Zhang, W., 2008. "An asset residual life prediction model based on expert judgments," European Journal of Operational Research, Elsevier, vol. 188(2), pages 496-505, July.
    4. Si, Xiao-Sheng & Wang, Wenbin & Hu, Chang-Hua & Zhou, Dong-Hua, 2011. "Remaining useful life estimation - A review on the statistical data driven approaches," European Journal of Operational Research, Elsevier, vol. 213(1), pages 1-14, August.
    5. Wang, Wenbin, 2007. "A two-stage prognosis model in condition based maintenance," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1177-1187, November.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. repec:eee:reensy:v:160:y:2017:i:c:p:21-36 is not listed on IDEAS
    2. Shengjin Tang & Chuanqiang Yu & Xue Wang & Xiaosong Guo & Xiaosheng Si, 2014. "Remaining Useful Life Prediction of Lithium-Ion Batteries Based on the Wiener Process with Measurement Error," Energies, MDPI, Open Access Journal, vol. 7(2), pages 1-28, January.
    3. repec:eee:reensy:v:168:y:2017:i:c:p:227-239 is not listed on IDEAS


    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:226:y:2013:i:1:p:53-66. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.