On an example of the reliability analysis of a steel girder was presented the problem of the invariance of the hybrid Monte Carlo (MC) simulation. The analysis was limited to determining the value of the reliability index β. The computations were carried out in two ways: on the grounds of the approximated value of the two first moments of the probability distribution of the accepted function of the g(X) limit state – ESM(Empirical Second Moment) or of empirical distribution function of the limit state function value g(X) – ECD (Empirical Cumulative Distribution). Each analysis was carried out for two identical forms of limit state function g1(X) i g2(X). The results obtained were compared and the findings lead to the conclusion that: the values of the reliability index β, computed with the ECD method are the same independently of the accepted function of the limit state gi(X); but computed with the ESM method, are in the majority of cases different. It means that analysis carried out with the ESM procedure is invariant in contrast the ECD procedure.

Keywords: reliability,Monte Carlomethod (MC), finite element method (FEM), artificial neural networks (ANN), steel girder.