Reliability Calculus on Crack Propagation Problem with a Markov Renewal Process
Résumé
This chapter concerns a stochastic differential system that describes the evolution of a degradation mechanism, the fatigue crack propagation. A Markov process will be considered as the perturbing process of the system that models the crack evolution. With the help of Markov renewal theory, we study the reliability of a structure and propose for it a new analytical solution. The method we propose reduces the complexity of the reliability calculus compared with the previous resolution method. As numerical applications, we tested our method on a numerical example and on an experimental data set, which gave results in good agreement with a Monte Carlo estimation.