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Piecewise deterministic Markov process for condition-based maintenance models — Application to critical infrastructures with discrete-state deterioration

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  • Arismendi, Renny
  • Barros, Anne
  • Grall, Antoine

Abstract

In recent decades, the technology and techniques for condition monitoring have experienced a rapid development. However, there is still a need for reducing unnecessary inspections and/or preventive maintenance actions and their associated cost, through optimal design of condition-based maintenance (CBM) strategies. Accordingly, mathematical modelling and optimization of CBM has become of interest for industry managers and researchers. This work explores on the application of a piecewise deterministic Markov process (PDMP) to encompass different modelling assumptions as non-negligible maintenance delays and inspection-based condition monitoring. These assumptions are relevant for many critical infrastructures in civil engineering or in oil & gas industry whose deterioration states are classified at a very high level of abstraction among a finite and small set of possible states. A formalism to model this type of problems is proposed in which the deterministic motion of the PDMP is reduced to a trivial differential equation to track the time elapsed between events. A numerical scheme for quantification, as an approximation of the Chapman–Kolmogorov equation, is presented. Later, an illustration case dealing with CBM of road bridges by the NPRA (Norwegian Public Roads Administration) is presented, guiding through the modelling and quantification approach.

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  • Arismendi, Renny & Barros, Anne & Grall, Antoine, 2021. "Piecewise deterministic Markov process for condition-based maintenance models — Application to critical infrastructures with discrete-state deterioration," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:reensy:v:212:y:2021:i:c:s0951832021000983
    DOI: 10.1016/j.ress.2021.107540
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    References listed on IDEAS

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    Cited by:

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    3. Pugliese, F. & De Risi, R. & Sarno, L. Di, 2022. "Reliability assessment of existing RC bridges with spatially-variable pitting corrosion subjected to increasing traffic demand," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    4. Wu, Xingguang & Huang, Huirong & Xie, Jianyu & Lu, Meixing & Wang, Shaobo & Li, Wang & Huang, Yixuan & Yu, Weichao & Sun, Xiaobo, 2023. "A novel dynamic risk assessment method for the petrochemical industry using bow-tie analysis and Bayesian network analysis method based on the methodological framework of ARAMIS project," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    5. Zhang, Aibo & Wu, Shengnan & Fan, Dongming & Xie, Min & Cai, Baoping & Liu, Yiliu, 2022. "Adaptive testing policy for multi-state systems with application to the degrading final elements in safety-instrumented systems," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    6. Karabağ, Oktay & Bulut, Önder & Toy, Ayhan Özgür & Fadıloğlu, Mehmet Murat, 2024. "An efficient procedure for optimal maintenance intervention in partially observable multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    7. Mosayebi Omshi, E. & Shemehsavar, S. & Grall, A., 2024. "An intelligent maintenance policy for a latent degradation system," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    8. GAO, Guibing & ZHOU, Dengming & TANG, Hao & HU, Xin, 2021. "An Intelligent Health diagnosis and Maintenance Decision-making approach in Smart Manufacturing," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    9. Sun, Tianqi & Vatn, Jørn, 2024. "A phase-type maintenance model considering condition-based inspections and maintenance delays," Reliability Engineering and System Safety, Elsevier, vol. 243(C).

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