Nova classe de modelos paramétricos para análise de sistemas reparáveis

Abstract

The Arithimetic Reduction of Age (ARA) model class from Doyen e Gaudoin (2004) has been widely used in the analysis of repairable systems, whose repair effect is expressed by an arithmetic age reduction. However, the class presupposes a state of degradation of the system, this condition implies β > 1 in the Power Law Process (PLP). However, there are cases in which the system improves (PLP with β < 1) up to a certain time. Its intensity after repairs remains parallel to the initial intensity, consequently, it fails to capture other forms of failure intensity. Given these limitations, we propose the modified ARA1 model (ARAM1), which makes it possible to model systems in the process of renovation or degradation, and we also propose a new generalized PLP process (PLPG), based on change points. From the PLPG it is possible to derive the main models with change points and with imperfect repair. New models are proposed from the PLPG, which we call completely imperfect repairs (RCI) and partially imperfect repairs (RPI(p)). Another advantage of this approach is that it allows the intensity after repairs not to remain parallel to the initial intensity, expanding its applications in the real world. Finally, we propose a new PLP reparameterization with time truncation to incorporate it into new models and thus obtain a better interpretation of its parameters. The estimators of the proposed model were obtained using the maximum likelihood method. We evaluated the performance of the parameter estimators through Monte Carlo (MC) simulations. For illustration purposes we consider actual failure times in applications. The proposed models indicated superiority to other models in the literature, which illustrates the importance of the new approaches.