.. _method-stoch_collocation-reliability_levels:

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reliability_levels
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Specify reliability levels at which the response values will be estimated


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

   method-stoch_collocation-reliability_levels-num_reliability_levels


**Specification**

- *Alias:* None

- *Arguments:* REALLIST

- *Default:* No CDF/CCDF response levels to compute


**Child Keywords:**

+-------------------------+--------------------+----------------------------+---------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword             | Dakota Keyword Description                  |
|                         | Group              |                            |                                             |
+=========================+====================+============================+=============================================+
| Optional                                     | `num_reliability_levels`__ | Specify which ``reliability_levels``        |
|                                              |                            | correspond to which response                |
+----------------------------------------------+----------------------------+---------------------------------------------+

.. __: method-stoch_collocation-reliability_levels-num_reliability_levels.html



**Description**


Response levels are calculated
for specified CDF/CCDF reliabilities by projecting out the prescribed
number of sample standard deviations from the sample mean.



**Theory**


Sets of response-probability pairs computed with the forward/inverse
mappings define either a cumulative distribution function (CDF) or a
complementary cumulative distribution function (CCDF) for each
response function.

In the case of evidence-based epistemic methods,
this is generalized to define either cumulative belief and
plausibility functions (CBF and CPF) or complementary cumulative
belief and plausibility functions (CCBF and CCPF) for each response
function.

An inverse mapping involves computing the belief and plausibility
response level for either a specified probability level or a specified
generalized reliability level (two results for each level mapping in
the evidence-based epistemic case, instead of the one result for each
level mapping in the aleatory case).