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Statistical modeling and reliability analysis of multiple repairable systems with dependent failure times under perfect repair

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  • Brito, Éder S.
  • Tomazella, Vera L.D.
  • Ferreira, Paulo H.

Abstract

In repairable systems, a fundamental aspect to be considered is to predict the reliability of the systems under study. Establishing reliability models for multiple repairable systems, however, is still a challenging problem when considering the dependency or unobserved heterogeneity of component failures. This paper focuses on a special repair assumption, called perfect repair, for repairable systems with dependent failures, where only the failed component is restored to as good as new condition. A frailty model is proposed to capture the statistical dependency and unobserved heterogeneity. The classical inferential method for estimating parameters and the reliability predictors will be shown for models in repairable systems under the assumption of perfect repair. An extensive simulation study is conducted under different scenarios to verify the suitability of the model and the asymptotic consistency and efficiency properties of the maximum likelihood estimators. The proposed methodology can be especially useful for industries that operate with repairable systems subjected to the replacement of parts after failures and to non-quantifiable factors that can interfere with the failure times of these parts. We illustrate the practical relevance of the proposed model on two real data sets. The first deals with a set of 9 sugarcane harvesters, observed during a fixed period of time, whose cutting blades failed several times in this interval. The other deals with a set of 5 dump trucks whose diesel engines also had recurring failures during the observation period. Parametric inference is carried out under the power-law process model that has found significant attention in industrial applications.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:222:y:2022:i:c:s0951832022000527
    DOI: 10.1016/j.ress.2022.108375
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    References listed on IDEAS

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    1. Safaei, Fatemeh & Ahmadi, Jafar & Balakrishnan, N., 2019. "A repair and replacement policy for repairable systems based on probability and mean of profits," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 143-152.
    2. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    3. Toledo, Maria Luíza Guerra de & Freitas, Marta A. & Colosimo, Enrico A. & Gilardoni, Gustavo L., 2015. "ARA and ARI imperfect repair models: Estimation, goodness-of-fit and reliability prediction," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 107-115.
    4. Klara Goethals & Paul Janssen & Luc Duchateau, 2008. "Frailty models and copulas: similarities and differences," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(9), pages 1071-1079.
    5. Almeida, Marco Pollo & Paixão, Rafael S. & Ramos, Pedro L. & Tomazella, Vera & Louzada, Francisco & Ehlers, Ricardo S., 2020. "Bayesian non-parametric frailty model for dependent competing risks in a repairable systems framework," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    6. Fu, Yuqiang & Zhu, Xiaoyan & Ma, Xiaoyang, 2020. "Optimum component reallocation and system replacement maintenance for a used system with increasing minimal repair cost," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    7. 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).
    8. Mosayebi Omshi, E. & Grall, A., 2021. "Replacement and imperfect repair of deteriorating system: Study of a CBM policy and impact of repair efficiency," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    9. Slimacek, Vaclav & Lindqvist, Bo Henry, 2016. "Nonhomogeneous Poisson process with nonparametric frailty," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 14-23.
    10. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
    11. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
    12. Chris Elbers & Geert Ridder, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(3), pages 403-409.
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    Cited by:

    1. Patawa, Rohit & Pundir, Pramendra Singh, 2023. "Inferential study of single unit repairable system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 503-516.
    2. 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).
    3. 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).
    4. Martón, I. & Sánchez, A.I. & Carlos, S. & Mullor, R. & Martorell, S., 2023. "Prognosis of wear-out effect on of safety equipment reliability for nuclear power plants long-term safe operation," Reliability Engineering and System Safety, Elsevier, vol. 233(C).

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