Reliability modelling and assessment by joint consideration of Petri nets and gamma deterioration processes

This article develops a new approach that integrates the gamma processes in Petri nets for modeling stochastic deterioration. In the area of reliability, it was shown that gamma processes are able to describe the physical degradation of components and, so, their importance in safety evaluation has been proved by many previous researches. First, a mathematical overview of the gamma process is given along with basic examples. Furthermore, a model of the gamma process on the basis of Petri nets is developed followed by an estimation of the remaining useful life (RUL) and the reliability of a single component. In this work, we propose to consider two cases for the estimation of the RUL: with and without knowledge of the level of degradation. Due to the knowledge of the degradation level, the evaluation of the reliability can be different and results are compared between them. Finally, a discussion about the application of both gamma process and Petri nets for describing the system behavior and its reliability assessment is presented explaining the value of the model in the current and the future industrial problems.