Conference article

This article proposes an efficient approach to model stochastic hybrid systems and to implement Monte Carlo simulation for such models; thus allowing the calculation of various probabilistic indicators: reliability; availability; average production; life cycle cost etc. First; we show that stochastic hybrid systems can be considered; most of the time; as Piecewise Deterministic Markov Processes (PDMP). Although PDMP have been long ago formalized and studied from a theoretical point of view; they are still difficult to use in real applications. The solution proposed here relies on a novel method to handle the case when the hazard rate of a transition depends on continuous variables; the use of an extension of Modelica 3.3 and on Monte Carlo simulation. We illustrate the approach with a simple example: a heating system subject to failures; for which we give the details of the modeling and some calculation results. We compare our ideas to other approaches reported in the literature.

Stochastic hybrid system; PDMP; dynamic reliability; state-dependent hazard rate; continuous time state-machine; Monte Carlo Simulation