mohamed eid

Modelling and estimating the reliability of stochastic dynamical systems with Markovian switching

Reliability Engineering & System Safety, 2008

Many engineering problems in structural reliability are formulated as stress strength models. One... more

Piecewise deterministic Markov processes applied to fatigue crack growth modelling

Journal of Statistical Planning and Inference, 2009

In this paper, we use a particular piecewise deterministic Markov process (PDMP) to model the evo... more In this paper, we use a particular piecewise deterministic Markov process (PDMP) to model the evolution of a degradation mechanism that may arise in various structural components, namely, the fatigue crack growth. We first derive some probability results on the stochastic dynamics with the help of Markov renewal theory: a closed-form solution for the transition function of the PDMP is given. Then, we investigate some methods to estimate the parameters of the dynamical system, involving Bogolyubov's averaging principle and maximum likelihood estimation for the infinitesimal generator of the underlying jump Markov process. Numerical applications on a real crack data set are given.

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Neutronic characterization of the MEGAPIE target

Annals of Nuclear Energy, 2009

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