.. _sphx_glr_api_gallery_reliability_structural:

Structural reliability
----------------------

The probability that a load exceeds a resistance.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Alfred Freudenthal (1947) argued that a safety factor, the ratio of mean strength to mean load, says nothing about safety on its own: two designs with the same factor can fail at very different rates if their loads and strengths scatter differently. What matters is the overlap of the two distributions. For independent normal strength S and stress s, R = P(S &gt; s) = \Phi(\beta) with \beta = (\mu_S - \mu_s)/\sqrt{\sigma_S^2 + \sigma_s^2} (~engineeringkit.reliability.stress_strength_reliability).">

.. only:: html

  .. image:: /api/gallery/reliability/structural/images/thumb/sphx_glr_plot_01_freudenthal_interference_thumb.png
    :alt:

  :doc:`/api/gallery/reliability/structural/plot_01_freudenthal_interference`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Freudenthal's stress-strength interference (1947)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Cornell&#x27;s 1969 index, mean over standard deviation of the safety margin g, has a flaw: it changes when the same failure condition is written differently, say R - S &lt; 0 or R/S - 1 &lt; 0. Hasofer and Lind (1974) fixed it by measuring, in standardised variables, the shortest distance from the mean to the failure surface itself (~engineeringkit.reliability.hasofer_lind_index). The nearest point, the design point, is where failure is most likely to happen, and p_f \approx \Phi(-\beta).">

.. only:: html

  .. image:: /api/gallery/reliability/structural/images/thumb/sphx_glr_plot_02_hasofer_lind_thumb.png
    :alt:

  :doc:`/api/gallery/reliability/structural/plot_02_hasofer_lind`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Hasofer and Lind's reliability index (1974)</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/reliability/structural/plot_01_freudenthal_interference
   /api/gallery/reliability/structural/plot_02_hasofer_lind