.. _method-sampling-tolerance_intervals:

"""""""""""""""""""
tolerance_intervals
"""""""""""""""""""



Computes the double sided tolerance interval equivalent normal distribuion.



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

   method-sampling-tolerance_intervals-coverage
   method-sampling-tolerance_intervals-confidence_level


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+----------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword       | Dakota Keyword Description                    |
|                         | Group              |                      |                                               |
+=========================+====================+======================+===============================================+
| Optional                                     | `coverage`__         | The coverage to be used for the calculation   |
|                                              |                      | of the lower and upper ends of the interval   |
|                                              |                      | covering the user supplied samples.           |
+----------------------------------------------+----------------------+-----------------------------------------------+
| Optional                                     | `confidence_level`__ | The confidence level to be used to determine  |
|                                              |                      | the standard deviation of the equivalent      |
|                                              |                      | normal distribution.                          |
+----------------------------------------------+----------------------+-----------------------------------------------+

.. __: method-sampling-tolerance_intervals-coverage.html
__ method-sampling-tolerance_intervals-confidence_level.html



**Description**



The "tolerance_intervals" keyword is used to compute (i) the equivalent
normal distribution, given response samples and a desired conficence level
between 0 and 1, and (ii) the lower and upper ends of an inverval covering
the samples, given a desired coverage between 0 and 1 :cite:p:`Jekel20`.

*Default Behavior*

By default, coverage is set to 0.95 (95%) and confidence level is set to 0.90 (90%).

*Expected Output*

Dakota first analyzes the N response samples supplied by the user, and
eliminates any sample with a NAN value, resulting in a final amount
M <= N of samples to be actually used in the calculations. If M >= 2,
then Dakota computes 6 values: the sample mean 'mu', the sample standard
deviation 's', the multiplicative factor 'f', the tolerance interval
lower end 'mu-f*s', the tolerance interval upper end 'mu+f*s', and the
standard deviation 's_equiv' of the tolerance interval equivalent normal.




**Examples**



.. code-block::

    method
      sampling
        samples 5
        refinement_samples 4 3 3
        sample_type random
        tolerance_intervals
          coverage 0.96
          confidence_level 0.92
        seed = 31415