Modelling and estimating the reliability of stochastic dynamical systems with Markovian switching

In this paper, a general framework for the modelling of physical phenomena with stochastic dynamical systems switched by jump Markov processes is given. A methodology of the associated estimation procedures is provided. A particular attention is paid to the estimation of the underlying jump process, which is not observable. As an application, a stochastic model is proposed for the fatigue crack growth problem. The estimation of the model parameters is made on a real crack growth data set. We are thus able to simulate some crack growth paths which are used for reliability analysis through Monte Carlo techniques.