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Parameter estimation in an ARD∞ Wiener degradation and maintenance model under different observation schemes

Author

Listed:
  • Lucía Bautista
  • Inma T. Castro
  • Christophe Bérenguer
  • Olivier Gaudoin
  • Laurent Doyen

Abstract

This paper develops a statistical inference study within a degradation model featuring imperfect maintenance for technological or industrial devices. Degrading systems undergo maintenance that only partially reduces their degradation level. The underlying degradation process of the system is modelled by using an univariate Wiener process with drift. The imperfect maintenance is modelled by using an Arithmetic Reduction of Degradation of infinite order model ( ARD ∞ ). The system is observed at different times and the degradation level of the system is recorded. The estimation study explores five different observation schemes. Our work focuses on the estimation of the model parameters under these observation schemes, deriving maximum likelihood estimators for each case. A simulation study assesses the quality of the estimators and compares the different observation schemes.

Suggested Citation

  • Lucía Bautista & Inma T. Castro & Christophe Bérenguer & Olivier Gaudoin & Laurent Doyen, 2026. "Parameter estimation in an ARD∞ Wiener degradation and maintenance model under different observation schemes," Journal of Risk and Reliability, , vol. 240(1), pages 261-277, February.
    • Handle: RePEc:sae:risrel:v:240:y:2026:i:1:p:261-277
    DOI: 10.1177/1748006X251348825
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    References listed on IDEAS

    as
    1. Wang, Xiao, 2010. "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 340-351, February.
    2. Zhang, Mimi & Gaudoin, Olivier & Xie, Min, 2015. "Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 245(2), pages 531-541.
    3. Wang, Xiaolin & Balakrishnan, Narayanaswamy & Guo, Bo, 2014. "Residual life estimation based on a generalized Wiener degradation process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 13-23.
    4. Yu, Wennian & Shao, Yimin & Xu, Jin & Mechefske, Chris, 2022. "An adaptive and generalized Wiener process model with a recursive filtering algorithm for remaining useful life estimation," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    5. Zhao, Xiujie & Chen, Piao & Gaudoin, Olivier & Doyen, Laurent, 2021. "Accelerated degradation tests with inspection effects," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1099-1114.
    6. MERCIER, Sophie & CASTRO, I.T., 2019. "Stochastic comparisons of imperfect maintenance models for a gamma deteriorating system," European Journal of Operational Research, Elsevier, vol. 273(1), pages 237-248.
    7. Xiujie Zhao & Olivier Gaudoin & Laurent Doyen & Min Xie, 2019. "Optimal inspection and replacement policy based on experimental degradation data with covariates," IISE Transactions, Taylor & Francis Journals, vol. 51(3), pages 322-336, March.
    8. Haitao Liao & Elsayed A. Elsayed, 2006. "Reliability inference for field conditions from accelerated degradation testing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(6), pages 576-587, September.
    9. Ye, Zhi-Sheng & Chen, Nan & Shen, Yan, 2015. "A new class of Wiener process models for degradation analysis," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 58-67.
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