Abstract
First-and second-order reliability methods have turned out to be efficient practical tools in structural reliability for direct probabilistic design or for the development of probability-based design codes. These methods are approximate but certain Monte Carlo techniques with importance sampling can make reliability estimates arbitrarily accurate. Three different methods are presented and tested at a suitable example with respect to their numerical efficiency. It is found that a method which also uses curvature information in the so-called most likely failure point usually is preferable to the alternatives if an update of first-or second-order estimates is necessary. However, that method becomes inadequate for very high problem dimensions and/or large failure probabilities.
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