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Bayesian gamma processes for optimizing condition‐based maintenance under uncertainty

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  • N. Bousquet
  • M. Fouladirad
  • A. Grall
  • C. Paroissin

Abstract

The aim of this article is twofold: (i) modeling partially observed crack growth of industrial components using gamma processes and (ii) providing estimators of the best maintenance time in a statistical Bayesian framework. The choice of a Bayesian framework is motivated by the small size of data, the availability of expert knowledge about the crack propagation, and more generally, the concern about the integration of parametrical uncertainties when optimizing a maintenance action. The article answers to the methodological question of Bayesian prior elicitation by adopting a strategy based on virtual data information and defines optimal replacement times as posterior Bayes estimators minimizing appropriate cost functions. More precisely, the industrial data are described, and two different levels of available information are considered. Then, the Bayesian parameter estimation procedure in each case is thoroughly explained, by conducting MCMC runs. Different criteria for maintenance optimization, taking account all uncertainties, are considered and discussed. The overall procedure is tested on simulated data and applied over a real dataset. Copyright © 2014 John Wiley & Sons, Ltd.

Suggested Citation

  • N. Bousquet & M. Fouladirad & A. Grall & C. Paroissin, 2015. "Bayesian gamma processes for optimizing condition‐based maintenance under uncertainty," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(3), pages 360-379, May.
    • Handle: RePEc:wly:apsmbi:v:31:y:2015:i:3:p:360-379
    DOI: 10.1002/asmb.2076
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    Cited by:

    1. 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).
    2. Yuan, Xian-Xun & Higo, Eishiro & Pandey, Mahesh D., 2021. "Estimation of the value of an inspection and maintenance program: A Bayesian gamma process model," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Wang, Jingjing & Qiu, Qingan & Wang, Huanhuan & Lin, Cong, 2021. "Optimal condition-based preventive maintenance policy for balanced systems," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    4. 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).
    5. 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).
    6. Khac Tuan Huynh & Antoine Grall, 2020. "A condition-based maintenance model with past-dependent imperfect preventive repairs for continuously deteriorating systems," Journal of Risk and Reliability, , vol. 234(2), pages 333-358, April.

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