Semi-Markov processes for reliability studies

We study the evolution of a multi-component system which is modeled by a semi-Markov process. We give formulas for the avaibility and the reliability of the system. In the r-positive case, we prove that the quasi-stationary probability on the working states is the normalised left eigenvector of some computable matrix and that the asymptotic failure rate is equal to the absolute value of the convergence parameter r

Dans le sol africain, de l'eau

D'après l'Unicef, plus de 2000 enfants, principalement africains, meurent chaque jour faute d'accès à l'eau potable. Un problème que les investissements internationaux n'ont jusque-là pas réussi à résoudre

Numerical methods for piecewise deterministic Markov processes with boundary

We study the approximation of the distribution of Piecewise Deterministic Markov Processes jumping when the process reaches some boundary of the domain. We first introduce an equation to which the marginal distributions of the process are solution, which generalizes Kolmogorov equations in this case. We then prove the uniqueness of this solution, and propose a finite volume numerical scheme for its approximation. This finite volume scheme enables the approximation of the asymptotic steady problem. We then prove the convergence of this numerical scheme to the marginal distributions of the process. We conclude this paper by some properties of the marginal distributions, directly resulting from the generalized Kolmogorov equation with boundary