document: 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
doc_bio_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: unit hypercube limit condition recursive method
abstractive_keyphrases: failure probabilities computation reliability analysis applications n-dimensional uniform random variable gauss-legendre quadrature formulae multiple integrals calculation tail approximation