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A condition‐based imperfect replacement policy for a periodically inspected system with two dependent wear indicators

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  • Sophie Mercier
  • Hai Ha Pham

Abstract

A two‐component system is considered, which is subject to accumulative deterioration. Because of common stress, the components are dependent. Their joint deterioration is modelled with a bivariate nondecreasing Lévy process. The deterioration level of both components is known only through perfect and periodic inspections. By an inspection, components with deterioration level beyond a specific threshold are instantaneously replaced by new ones (corrective or preventive replacements). Otherwise, they are left as they are. Between inspections, failures remain unrevealed. This replacement policy is classical in a univariate setting, with deterioration modelled by a Gamma process. In the bivariate case, it leads to imperfect repairs at the system level, which highly complicates the study. The replacement policy is assessed through cost functions on both finite and infinite horizons, which take into account some economical dependence between components. Markov renewal theory is used to study the behaviour of the system, in a continuous and bivariate setting. Numerical experiments illustrate the study, considering a specific Lévy process with univariate Gamma processes as margins. Although technical details are not provided here for the numerical computations, the paper shows that there is a technical gap between the traditional one‐dimensional studies and the present two‐dimensional one, especially for the computation of the asymptotic distribution of the underlying Markov chain. Hence, there is a need for further development in the bivariate (or multivariate) setting. Copyright © 2014 John Wiley & Sons, Ltd.

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  • Sophie Mercier & Hai Ha Pham, 2014. "A condition‐based imperfect replacement policy for a periodically inspected system with two dependent wear indicators," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(6), pages 766-782, November.
    • Handle: RePEc:wly:apsmbi:v:30:y:2014:i:6:p:766-782
    DOI: 10.1002/asmb.2011
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    Cited by:

    1. Zhang, Aibo & Zhang, Tieling & Barros, Anne & Liu, Yiliu, 2020. "Optimization of maintenances following proof tests for the final element of a safety-instrumented system," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    2. Dias, Luis & Leitão, Armando & Guimarães, Luis, 2021. "Resource definition and allocation for a multi-asset portfolio with heterogeneous degradation," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    3. Zhang, Nan & Fouladirad, Mitra & Barros, Anne & Zhang, Jun, 2020. "Condition-based maintenance for a K-out-of-N deteriorating system under periodic inspection with failure dependence," European Journal of Operational Research, Elsevier, vol. 287(1), pages 159-167.
    4. Petchrompo, Sanyapong & Parlikad, Ajith Kumar, 2019. "A review of asset management literature on multi-asset systems," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 181-201.
    5. Liu, Bin & Pandey, Mahesh D. & Wang, Xiaolin & Zhao, Xiujie, 2021. "A finite-horizon condition-based maintenance policy for a two-unit system with dependent degradation processes," European Journal of Operational Research, Elsevier, vol. 295(2), pages 705-717.
    6. Castro, Inma T. & Basten, Rob J.I. & van Houtum, Geert-Jan, 2020. "Maintenance cost evaluation for heterogeneous complex systems under continuous monitoring," Reliability Engineering and System Safety, Elsevier, vol. 200(C).
    7. Zhang, Nan & Cai, Kaiquan & Zhang, Jun & Wang, Tian, 2022. "A condition-based maintenance policy considering failure dependence and imperfect inspection for a two-component system," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    8. Huynh, K.T. & Vu, H.C. & Nguyen, T.D. & Ho, A.C., 2022. "A predictive maintenance model for k-out-of-n:F continuously deteriorating systems subject to stochastic and economic dependencies," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    9. 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.
    10. Wang, Yukun & Li, Xiaopeng & Chen, Junyan & Liu, Yiliu, 2022. "A condition-based maintenance policy for multi-component systems subject to stochastic and economic dependencies," Reliability Engineering and System Safety, Elsevier, vol. 219(C).

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