Development of a mixed model using generalized renewal processes and the weibull distribution

Abstract

In order to analyze interventions in repairable systems, the literature contains several methodologies aiming to model the behavior of times between interventions. Such interventions can be modeled by Point Stochastic Processes in order to analyze the probabilistic behavior of times between events. Specifically, the Generalized Renewal Processes allow the study of times between interventions by measuring the quality of each intervention and the response of the system to these interventions — this is done by using the concept of virtual age. In such concept it is possible to apply two kinds of Kijima models (Type I and II). Therefore, this work presents a model capable of study the quality of interventions using up of a mix between the two Kijima models where it is possible to capture the performance on each of these interventions proportionally. Specifically, a new approach to virtual age of Kijima models is presented as well as mathematical properties of the Generalized Renewal Process using the Weibull distribution probability. Finally, the applicability of the model is checked in real data from some problems found in the literature.