Dynamical systems with semi-Markovian perturbations and their use in structural reliability

Chapter 10The aim of this chapter is to present dynamical systems evolving in continuous-time and perturbed by semi-Markov processes (SMP). We investigate both probabilistic modeling and statistical estimation of such models. This work was initially developed in order to study cracking problems for the confinement device in nuclear power plants, where a jump Markov process was used as the perturbing process. The new key element here is the use of SMPs instead of Markov ones for the randomization of the system. Several numerical illustrations in reliability are investigated, accompanied with guidelines for a practical numerical implementation