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
.