Introduction
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The numerical Monte Carlo method consists in doing :math:`\mathit{Ns}` numerical simulations of the mechanical model in order to evaluate the statistical quantities of the calculation results. The 3 main steps in propagating uncertainties by Monte Carlo simulation are:


* Uncertainty modeling: Generation of a sample of :math:`\text{Ns}` realizations of random data as input to the mechanical model (random parameters and stochastic processes),


* The propagation of uncertainties: Calculation of the :math:`\text{Ns}` result quantities corresponding to these data,


* The calculation of statistical estimators of the quantities sought: mean, standard deviation, fractions...; evaluation of seismic fragility curves.

As part of a mechanical study with Code_Aster, you can use the distribution functionalities of parametric studies in order to carry out such a probabilistic analysis. Indeed, in the current case where the :math:`\mathit{Ns}` prints and mechanical simulations are independent, we can first establish an experimental plan of the case studies to be launched. The :math:`\mathit{Ns}` corresponding studies are then launched, and the statistical quantities are calculated by post-processing the results.

The approach and its implementation with*Code_Aster* are described in this document.