Stochastic hybrid automata model for dynamic reliability assessment

A dynamic hybrid system is described by a set of continuous variables and a set of discrete events interacting together. The reality also requires taking into account component failures and the stochastic behaviour of the system. Some events or variables then take a stochastic character. The current paper presents the concept of a stochastic hybrid automaton (SHA) and its abilities to handle interactions between component failures, physical variables of the process, and operating modes of the system. Its use as a tool for Monte Carlo simulation that allows the evaluation of dependability parameters in a dynamic context is proposed. As a validation, the SHA approach has been applied to a benchmark problem studied by some other authors using different techniques (continuous cell-to-cell mapping technique, stochastic Petri nets, and piecewise deterministic Markov processes). The main interest is to show how the dependency between the probability distribution of a component failure and a physical continuous variable (temperature) may be handled. As an illustration of its other abilities, the SHA approach has been applied to a second application including particular components with multiple ageing modes. In this example the main interest is to highlight the problems of the modelling and the dependability assessment of a hybrid dynamic system.