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Statistical inference for imperfect maintenance models with missing data

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  • Dijoux, Yann
  • Fouladirad, Mitra
  • Nguyen, Dinh Tuan

Abstract

The paper considers complex industrial systems with incomplete maintenance history. A corrective maintenance is performed after the occurrence of a failure and its efficiency is assumed to be imperfect. In maintenance analysis, the databases are not necessarily complete. Specifically, the observations are assumed to be window-censored. This situation arises relatively frequently after the purchase of a second-hand unit or in the absence of maintenance record during the burn-in phase. The joint assessment of the wear-out of the system and the maintenance efficiency is investigated under missing data. A review along with extensions of statistical inference procedures from an observation window are proposed in the case of perfect and minimal repair using the renewal and Poisson theories, respectively. Virtual age models are employed to model imperfect repair. In this framework, new estimation procedures are developed. In particular, maximum likelihood estimation methods are derived for the most classical virtual age models. The benefits of the new estimation procedures are highlighted by numerical simulations and an application to a real data set.

Suggested Citation

  • Dijoux, Yann & Fouladirad, Mitra & Nguyen, Dinh Tuan, 2016. "Statistical inference for imperfect maintenance models with missing data," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 84-96.
    • Handle: RePEc:eee:reensy:v:154:y:2016:i:c:p:84-96
    DOI: 10.1016/j.ress.2016.05.017
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    References listed on IDEAS

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    6. Yu, Jun-Wu & Tian, Guo-Liang & Tang, Man-Lai, 2008. "Statistical inference and prediction for the Weibull process with incomplete observations," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1587-1603, January.
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    Citations

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    Cited by:

    1. Maxim Finkelstein & Ji Hwan Cha, 2021. "On degradation-based imperfect repair and induced generalized renewal processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1026-1045, December.
    2. Liu, Yu & Chen, Yiming & Jiang, Tao, 2020. "Dynamic selective maintenance optimization for multi-state systems over a finite horizon: A deep reinforcement learning approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 166-181.
    3. Beutner, Eric, 2023. "A review of effective age models and associated non- and semiparametric methods," Econometrics and Statistics, Elsevier, vol. 28(C), pages 105-119.
    4. Xu, Hao & Gardoni, Paolo, 2020. "Conditional formulation for the calibration of multi-level random fields with incomplete data," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    5. Wakiru, James M. & Pintelon, Liliane & Muchiri, Peter N. & Chemweno, Peter K., 2019. "A simulation-based optimization approach evaluating maintenance and spare parts demand interaction effects," International Journal of Production Economics, Elsevier, vol. 208(C), pages 329-342.
    6. Brenière, Léa & Doyen, Laurent & Bérenguer, Christophe, 2020. "Virtual age models with time-dependent covariates: A framework for simulation, parametric inference and quality of estimation," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    7. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    8. Liu, Xingheng & Vatn, Jørn & Dijoux, Yann & Toftaker, Håkon, 2020. "Unobserved heterogeneity in stable imperfect repair models," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    9. Wakiru, James & Pintelon, Liliane & Muchiri, Peter N. & Chemweno, Peter K., 2021. "Integrated remanufacturing, maintenance and spares policies towards life extension of a multi-component system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).

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