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In the reliability theory, the availability of a component, characterized by non constant failure and repair rates, is obtained, at a given time, thanks to the computation of the marginal distributions of a semi-Markov process. These measures are shown to satisfy classical transport equations, the approximation of which can be done thanks to a finite volume method. Within a uniqueness result for the continuous solution, the convergence of the numerical scheme is then proven in the weak measure sense,...
In the reliability theory, the availability of
a component, characterized by non constant failure and repair rates,
is obtained, at a given time, thanks to the computation of the marginal distributions of a
semi-Markov process. These measures are shown to satisfy classical
transport equations, the approximation of which can be done
thanks to a finite volume method.
Within a uniqueness result for the continuous solution,
the convergence of the numerical scheme is
then proven in the weak measure...
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.
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