Frailty model for multiple repairable systems hierarchically represented subject to competing risks

In this paper, we propose a statistical model to describe the behaviour of failure times associated with groups of repairable systems hierarchically represented, under a competing risks framework, considering the existence of unobserved heterogeneity that acts individually on systems of each group, as well as the possibility of imperfect repairs whose initial failure rate is in the form of the power law. In this context for the unobserved heterogeneity in the groups, we consider the multiplicative frailty. To illustrate the use of the proposed model, we consider a database with the failures of 38 agricultural machines categorized into five different groups. We understand that the tractor fleet corresponds to the farm's agricultural system, therefore the need for intervention in this system occurs with the failure of any unit, individually, in a serial structure, of competing risks.e 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 analysing the results under a parallel structure.