Computing failure probabilities. Applications to reliability analysis

The paper presents one method for calculating failure probabilities with applications to reliability analysis. The method is based on transforming the initial set of variables to a n-dimensional uniform random variable in the unit hypercube, together with the limit condition set and calculating the associated probability using a recursive method based on the Gauss–Legendre quadrature formulas to calculate the resulting multiple integrals. An example of application is used to illustrate the proposed method.