Reliability of repairable systems with Non-Central Gamma frailty

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Adriane Caroline Teixeira Portela
Éder Silva de Brito
Vera Lucia Damasceno Tomazella
Carlos Alberto Ribeiro Diniz
Paulo Henrique Ferreira


Maintenance actions on industrial equipment are essential to reduce expenses associated with equipment failures. Based on a well-fitted model, it is possible, through the estimated parameters, to predict several functions of interest, such as the cumulative average and reliability functions. In this paper, a new frailty model is proposed to analyze failure times of repairable systems subject to unobserved heterogeneity actions. The Non-Central Gamma distribution is assumed to the frailty random variable effect. The class of minimal repair models for repairable systems is explored considering an approach that includes the frailty term to estimate the unobserved heterogeneity over the systems’ failure process. Classical inferential methods were used to parameter estimation and define the reliability prediction functions. A simulation study was conducted to confirm the properties expected in the estimators. Two real-world data known in literature were used to illustrate the estimation procedures and validate the proposed model as a viable alternative to those already established in the literature. The results obtained highlight the potential of our proposed approach, particularly for industries dealing with such systems, where unquantifiable factors may impact equipment failure times.

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Teixeira Portela, A. C., Brito, Éder S. de, Damasceno Tomazella, V. L., Ribeiro Diniz, C. A., & Ferreira, P. H. (2024). Reliability of repairable systems with Non-Central Gamma frailty. Brazilian Journal of Biometrics, 42(2), 182–201.


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