Reliability Index¶
The generalized reliability index
is used under the
following context:
is a probabilistic input vector,
its joint density probability,
a
deterministic vector,
the limit state
function of the model,
the event considered here and g(,) = 0 its boundary.
The probability content of the event
is
:
(1)¶
The generalized reliability index is defined as:
As
increases,
decreases rapidly.
These indices are available:
the FORM reliability index, where
is obtained with a FORM approximation (refer to ~): in this case, the generalized reliability index is equal to the Hasofer-Lindt reliability index
, which is the distance of the design point from the origin of the standard space,
the SORM reliability index, where
is obtained with a SORM approximation : Breitung, Hohenbichler or Tvedt (refer to ),
the generalized reliability index, where
is obtained with another technique : Monte Carlo simulations, importance samplings,…