:orphan:

.. _Reliability:

Reliability
===========



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Central dispersion
------------------



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    <div class="sphx-glr-thumbcontainer" tooltip="Evaluate the mean of a random vector by simulations">

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  .. image:: /auto_reliability/central_dispersion/images/thumb/sphx_glr_plot_expectation_simulation_algorithm_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_central_dispersion_plot_expectation_simulation_algorithm.py`

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      <div class="sphx-glr-thumbnail-title">Evaluate the mean of a random vector by simulations</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Analyse the central tendency of a cantilever beam">

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  .. image:: /auto_reliability/central_dispersion/images/thumb/sphx_glr_plot_central_tendency_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_central_dispersion_plot_central_tendency.py`

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      <div class="sphx-glr-thumbnail-title">Analyse the central tendency of a cantilever beam</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Estimate moments from Taylor expansions">

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  .. image:: /auto_reliability/central_dispersion/images/thumb/sphx_glr_plot_estimate_moments_taylor_thumb.svg
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  :ref:`sphx_glr_auto_reliability_central_dispersion_plot_estimate_moments_taylor.py`

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      <div class="sphx-glr-thumbnail-title">Estimate moments from Taylor expansions</div>
    </div>


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Reliability analysis
--------------------



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    <div class="sphx-glr-thumbcontainer" tooltip="Simulate an Event">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_event_manipulation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_event_manipulation.py`

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      <div class="sphx-glr-thumbnail-title">Simulate an Event</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Use a randomized QMC algorithm">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_estimate_probability_randomized_qmc_thumb.png
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_estimate_probability_randomized_qmc.py`

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      <div class="sphx-glr-thumbnail-title">Use a randomized QMC algorithm</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Estimate a probability with Monte Carlo">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_estimate_probability_monte_carlo_thumb.png
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_estimate_probability_monte_carlo.py`

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      <div class="sphx-glr-thumbnail-title">Estimate a probability with Monte Carlo</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Use the Adaptive Directional Stratification Algorithm">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_estimate_probability_adaptive_directional_sampling_thumb.png
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_estimate_probability_adaptive_directional_sampling.py`

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      <div class="sphx-glr-thumbnail-title">Use the Adaptive Directional Stratification Algorithm</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Use the post-analytical importance sampling algorithm">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_post_analytical_importance_sampling_thumb.png
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_post_analytical_importance_sampling.py`

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      <div class="sphx-glr-thumbnail-title">Use the post-analytical importance sampling algorithm</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Use the Directional Sampling Algorithm">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_estimate_probability_directional_sampling_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_estimate_probability_directional_sampling.py`

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      <div class="sphx-glr-thumbnail-title">Use the Directional Sampling Algorithm</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Estimate a flooding probability">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_flood_model_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_flood_model.py`

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      <div class="sphx-glr-thumbnail-title">Estimate a flooding probability</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create a threshold event">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_create_threshold_event_thumb.svg
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_create_threshold_event.py`

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      <div class="sphx-glr-thumbnail-title">Create a threshold event</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Specify a simulation algorithm">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_probability_simulation_parametrization_thumb.png
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_probability_simulation_parametrization.py`

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      <div class="sphx-glr-thumbnail-title">Specify a simulation algorithm</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Use the Importance Sampling algorithm">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_estimate_probability_importance_sampling_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_estimate_probability_importance_sampling.py`

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      <div class="sphx-glr-thumbnail-title">Use the Importance Sampling algorithm</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_axial_stressed_beam_quickstart_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_axial_stressed_beam_quickstart.py`

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      <div class="sphx-glr-thumbnail-title">Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Estimate a buckling probability">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_stiffened_panel_thumb.svg
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_stiffened_panel.py`

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      <div class="sphx-glr-thumbnail-title">Estimate a buckling probability</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Exploitation of simulation algorithm results">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_probability_simulation_results_thumb.svg
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_probability_simulation_results.py`

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      <div class="sphx-glr-thumbnail-title">Exploitation of simulation algorithm results</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Use the FORM algorithm in case of several design points">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_multi_form_thumb.svg
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_multi_form.py`

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      <div class="sphx-glr-thumbnail-title">Use the FORM algorithm in case of several design points</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Subset Sampling">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_subset_sampling_thumb.svg
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_subset_sampling.py`

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      <div class="sphx-glr-thumbnail-title">Subset Sampling</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Use the FORM - SORM algorithms">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_estimate_probability_form_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_estimate_probability_form.py`

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      <div class="sphx-glr-thumbnail-title">Use the FORM - SORM algorithms</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create a domain event">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_create_domain_event_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_create_domain_event.py`

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      <div class="sphx-glr-thumbnail-title">Create a domain event</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Non parametric Adaptive Importance Sampling (NAIS)">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_nais_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_nais.py`

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      <div class="sphx-glr-thumbnail-title">Non parametric Adaptive Importance Sampling (NAIS)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Test the design point with the Strong Maximum Test">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_strong_maximum_test_thumb.png
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_strong_maximum_test.py`

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      <div class="sphx-glr-thumbnail-title">Test the design point with the Strong Maximum Test</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Time variant system reliability problem">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_proba_system_event_thumb.svg
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_proba_system_event.py`

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      <div class="sphx-glr-thumbnail-title">Time variant system reliability problem</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Estimate a probability using Line Sampling">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_line_sampling_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_line_sampling.py`

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      <div class="sphx-glr-thumbnail-title">Estimate a probability using Line Sampling</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create unions or intersections of events">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_event_system_thumb.svg
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_event_system.py`

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      <div class="sphx-glr-thumbnail-title">Create unions or intersections of events</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Axial stressed beam : comparing different methods to estimate a probability">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_axial_stressed_beam_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_axial_stressed_beam.py`

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      <div class="sphx-glr-thumbnail-title">Axial stressed beam : comparing different methods to estimate a probability</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Cross Entropy Importance Sampling">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_crossentropy_thumb.svg
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  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_crossentropy.py`

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      <div class="sphx-glr-thumbnail-title">Cross Entropy Importance Sampling</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="An illustrated example of a FORM probability estimate">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_form_explained_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_form_explained.py`

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      <div class="sphx-glr-thumbnail-title">An illustrated example of a FORM probability estimate</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Using the FORM - SORM algorithms on a nonlinear function">

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  .. image:: /auto_reliability/reliability_analysis/images/thumb/sphx_glr_plot_estimate_probability_form_oscillator_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_analysis_plot_estimate_probability_form_oscillator.py`

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      <div class="sphx-glr-thumbnail-title">Using the FORM - SORM algorithms on a nonlinear function</div>
    </div>


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    </div>


Reliability processes
---------------------



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    <div class="sphx-glr-thumbcontainer" tooltip="Create an event based on a process">

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  .. image:: /auto_reliability/reliability_processes/images/thumb/sphx_glr_plot_event_process_thumb.png
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_processes_plot_event_process.py`

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      <div class="sphx-glr-thumbnail-title">Create an event based on a process</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Estimate a process-based event probability">

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  .. image:: /auto_reliability/reliability_processes/images/thumb/sphx_glr_plot_estimate_probability_monte_carlo_process_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_processes_plot_estimate_probability_monte_carlo_process.py`

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      <div class="sphx-glr-thumbnail-title">Estimate a process-based event probability</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Estimate Sobol indices on a field to point function">

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  .. image:: /auto_reliability/reliability_processes/images/thumb/sphx_glr_plot_field_fca_sobol_thumb.svg
    :alt:

  :ref:`sphx_glr_auto_reliability_reliability_processes_plot_field_fca_sobol.py`

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      <div class="sphx-glr-thumbnail-title">Estimate Sobol indices on a field to point function</div>
    </div>


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    </div>


.. toctree::
   :hidden:
   :includehidden:


   /auto_reliability/central_dispersion/index.rst
   /auto_reliability/reliability_analysis/index.rst
   /auto_reliability/reliability_processes/index.rst