Abstract
Abstract Efficient computational methods based on first and second order approximations (FORM/SORM) of the tails of a random variable, which is defined as a function of a set of basic variables, are given. Interesting examples of these types of functions are the probabilities of occurrence of the root events of fault trees or nodes in a Bayesian network. The method allows estimation of extreme percentiles and high confidence one-sided probability intervals of the target variables. Several examples of applications to real cases are used to illustrate the whole process.
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