The performance of a new, fast probability integration method which combines an improved equivalent normal concept and a scheme for linearizing a quadratic limit state is carefully examined. The examples tested include various combinations of linear and nonlinear limit states with normal and non-normal variables; some examples are considered the worst possible cases. It is demonstrated that the new method is able to provide accurate probability-of-failure estimates for most cases and performs reasonably well when the Rackwitz-Fiessler method produces severe errors.

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