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Unobserved heterogeneity in stable imperfect repair models

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  • Liu, Xingheng
  • Vatn, Jørn
  • Dijoux, Yann
  • Toftaker, HÃ¥kon

Abstract

This study investigates the effect of heterogeneity on the failures of repairable systems that undergo imperfect repairs, which are extensively used in reliability engineering. When considering a group of similar systems, the assumption that the repair processes are independent and identically distributed becomes questionable owing to the unobserved heterogeneity in these systems. The basic model we consider is the Kijima type II virtual age process with constant repair efficiency and a Weibull baseline distribution. We use the frailty models to study the heterogeneity between the systems and, in particular, the gamma-distributed frailty is investigated. We thus derive the asymptotic properties of the mixed repair process and corresponding likelihood estimates, and then evaluate the effects on the model parameter estimation process when heterogeneity is erroneously ignored. Furthermore, when the model is established correctly by accounting for the gamma distribution, we find that the maximum likelihood estimator is inconsistent and propose an alternative approach. Three case studies are presented to illustrate the benefits of taking account of unobserved heterogeneity in the estimation of the aging speed and reliability of assets and in scheduling preventive maintenance activities.

Suggested Citation

  • Liu, Xingheng & Vatn, Jørn & Dijoux, Yann & Toftaker, HÃ¥kon, 2020. "Unobserved heterogeneity in stable imperfect repair models," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:reensy:v:203:y:2020:i:c:s0951832020305408
    DOI: 10.1016/j.ress.2020.107039
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    Cited by:

    1. Zhang, Jingqi & Fouladirad, Mitra & Limnios, Nikolaos, 2025. "Sensitivity analysis of an imperfect maintenance policy for Proton-exchange membrane fuel cell based on geometric a semi-Markov model," Reliability Engineering and System Safety, Elsevier, vol. 255(C).
    2. Lu, Biao & Chen, Zhen & Zhao, Xufeng, 2021. "Data-driven dynamic predictive maintenance for a manufacturing system with quality deterioration and online sensors," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    3. Jiang, Renyan & Li, Fengping & Xue, Wei & Cao, Yu & Zhang, Kunpeng, 2023. "A robust mean cumulative function estimator and its application to overhaul time optimization for a fleet of heterogeneous repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    4. Maxim Finkelstein & Ji Hwan Cha, 2021. "Rejoinder to “Virtual age, is it real?”," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 37(1), pages 45-52, January.
    5. Brito, Éder S. & Tomazella, Vera L.D. & Ferreira, Paulo H., 2022. "Statistical modeling and reliability analysis of multiple repairable systems with dependent failure times under perfect repair," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    6. Wang, Yangpeng & Li, Shuxiang & Lee, Kangkuen & Tam, Hwayaw & Qu, Yuanju & Huang, Jingyin & Chu, Xianghua, 2023. "Accident risk tensor-specific covariant model for railway accident risk assessment and prediction," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    7. Ait Mokhtar, El Hassene & Laggoune, Radouane & Chateauneuf, Alaa, 2023. "Imperfect maintenance modeling and assessment of repairable multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    8. Syamsundar, A. & Naikan, V.N.A. & Wu, Shaomin, 2021. "Extended Arithmetic Reduction of Age Models for the Failure Process of a Repairable System," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    9. Brenière, Léa & Doyen, Laurent & Bérenguer, Christophe, 2023. "Optimization of preventive replacements dates and covariate inspections for repairable systems in varying environments," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1126-1141.

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