.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_reliability_sensitivity/reliability/plot_estimate_probability_randomized_qmc.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <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:


Use a randomized QMC algorithm
==============================

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

.. GENERATED FROM PYTHON SOURCE LINES 9-14

.. code-block:: Python

    from openturns.usecases import cantilever_beam
    import openturns as ot

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 15-16

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

.. GENERATED FROM PYTHON SOURCE LINES 16-18

.. code-block:: Python

    cb = cantilever_beam.CantileverBeam()








.. GENERATED FROM PYTHON SOURCE LINES 19-20

We load the joint probability distribution of the input parameters :

.. GENERATED FROM PYTHON SOURCE LINES 20-22

.. code-block:: Python

    distribution = cb.distribution








.. GENERATED FROM PYTHON SOURCE LINES 23-24

We load the model as well,

.. GENERATED FROM PYTHON SOURCE LINES 24-26

.. code-block:: Python

    model = cb.model








.. GENERATED FROM PYTHON SOURCE LINES 27-28

We create the event whose probability we want to estimate.

.. GENERATED FROM PYTHON SOURCE LINES 30-34

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 35-36

Define the low discrepancy sequence.

.. GENERATED FROM PYTHON SOURCE LINES 38-40

.. code-block:: Python

    sequence = ot.SobolSequence()








.. GENERATED FROM PYTHON SOURCE LINES 41-42

Create a simulation algorithm.

.. GENERATED FROM PYTHON SOURCE LINES 44-51

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 52-53

Retrieve results.

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.. code-block:: Python

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




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

 .. code-block:: none

    Pf= 0.0





.. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_estimate_probability_randomized_qmc.py:

.. only:: html

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

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

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

    .. 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>`