.. _method-local_reliability-mpp_search-integration-first_order:

"""""""""""
first_order
"""""""""""


First-order integration scheme



**Topics**


reliability_methods


.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* None


**Description**


First-order integration in local reliability methods uses the minimum Euclidean distance
from the origin to the most probable point (MPP) in transformed space to compute the probability of failure.
This distance, commonly called the reliability index Beta, is used to calculate the probability of failure
by calculating the standard normal cumulative distribution function at -Beta.


