In this work we propose a statistical model to understand the behavior of failure times associated with groups of repairable systems hierarchically represented, under a competing risks framework, with the consideration of the existence of unobserved heterogeneity that acts individually on the systems of each group, and also the possibility of imperfect repairs whose initial failure rate is in the form of the power law. In this context the unobserved heterogeneity in the groups we consider the model of multiplicative frailty. To illustrate the use of the proposed model, we consider a database with the failures of 38 agricultural machines categorized in five different groups. We understand that the tractor fleet corresponds to the farm's agricultural system, so the need for intervention in this system occurs with the failure of any unit, individually, in a serial structure, of competing risks. On the other hand, the understanding of the time in which all the machinery that makes up the fleet will have required some intervention is obtained by analyzing the results under a parallel structure.
