.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py:


Estimate a probability using randomized QMC
===========================================

In this example we are going to estimate a failure probability on the :ref:`cantilever beam <use-case-cantilever-beam>`.


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








We load the data class containing the probabilistic modeling of the beam.


.. code-block:: default

    from openturns.usecases import cantilever_beam as cantilever_beam
    cb = cantilever_beam.CantileverBeam()








We load the joint probability distribution of the input parameters :


.. code-block:: default

    distribution = cb.distribution








We load the model as well,


.. code-block:: default

    model = cb.model








We create the event whose probability we want to estimate.


.. code-block:: default

    vect = ot.RandomVector(distribution)
    G = ot.CompositeRandomVector(model, vect)
    event = ot.ThresholdEvent(G, ot.Greater(), 0.3)








Define the low discrepancy sequence.


.. code-block:: default

    sequence = ot.SobolSequence()








Create a simulation algorithm.


.. code-block:: default

    experiment = ot.LowDiscrepancyExperiment(sequence, 1)
    experiment.setRandomize(True)
    algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
    algo.setMaximumCoefficientOfVariation(0.05)
    algo.setMaximumOuterSampling(int(1e5))
    algo.run()








Retrieve results.


.. code-block:: default

    result = algo.getResult()
    probability = result.getProbabilityEstimate()
    print('Pf=', probability)




.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    Pf= 0.0





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  1.028 seconds)


.. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: plot_estimate_probability_randomized_qmc.py <plot_estimate_probability_randomized_qmc.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: plot_estimate_probability_randomized_qmc.ipynb <plot_estimate_probability_randomized_qmc.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_