A finite-volume scheme for dynamic reliability models

^** Email: christiane.cocozza{at}univ-mlv.fr^*** Email: robert.eymard{at}univ-mlv.fr^**** Email: sophie.mercier{at}univ-mlv.fr In a model arising in the dynamic reliability study of a system,the probability of the state of the system is completely describedby the Chapman–Kolmogorov equations, which are scalarlinear hyperbolic partial differential equations coupled bytheir right-hand side, the solution of which are probabilitymeasures. We propose in this paper a finite-volume scheme toapproximate these measures. We show, thanks to the proof ofthe tightness of the approximate solution, that the conservationof the probability mass leads to a compactness property. Theconvergence of the scheme is then obtained in the space of continuousfunctions with respect to the time variable, valued in the setof probability measures on graphic: see PDF] . We finally show on a numerical example the accuracy and efficiencyof the approximation method.