Reliability Index¶
The generalized reliability index is used under the following context: let be a probabilistic input vector with joint density probability , let be the limit state function of the model and let be an event whose probability is defined as:
(1)¶
The generalized reliability index is defined as:
where is the CDF of the normal distribution with zero mean and unit variance.
As increases, decreases rapidly.
According to the method used to evaluate , the generalized reliability index differs:
when has been obtained from the FORM approximation, then is equal to the Hasofer-Lindt reliability index , which is the distance of the design point from the origin of the standard space,
when has been obtained from a SORM approximation, then is equal to , or ,
when has been obtained from another technique (Monte Carlo simulations, importance samplings,…), we get the generalized index .