# Reliability Index¶

The generalized reliability index is used under the following context: let be a probabilistic input vector with joint density probability , let be a deterministic vector, 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 .