Abstract

In this paper, we seek to propose a model that allows us to evaluate the failure times of a single repairable system represented hierarchically, exposed to competing risks and under a minimal repair framework. Our study can be regarded as an extension of the research presented in Louzada et al. (2019), which comprises the representation of complex systems through a hierarchical structure in series and/or in parallel. For this, we deduce the general form of the model, as well as the likelihood function associated with it, to obtain reliable estimates for the parameters that index the model. In addition, we display the mechanism for generating random numbers based on the presented structure, which enables obtaining point and interval estimates (via parametric bootstrap) in a more convenient way for reliability curves at any level of the system hierarchy. We conduct an extensive Monte Carlo simulation study to evaluate the performance of the proposed maximum likelihood estimators and confidence intervals for the model parameters. Finally, we illustrate the applicability of our model and methods with applications that deal with the reliability modeling of a robotic unit still under development, resulting from a project carried out in partnership between Petrobras and other Brazilian research centers.