.. image:: images/logo.png

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ROCOF
'''''

Rate of occurrence of failures (ROCOF) is used to model the trend (constant, increasing, decreasing) in the failure interarrival times. For a repairable system, we want the ROCOF to be improving (failure interarrival times to be increasing). As failure times can often appear quite random, it is necessary to conduct a statistical test to determine if there is a statistically significant trend, and if there is a trend we can then model that trend using a Power Law NHPP. The test for statistical significance is the Laplace test which compares the Laplace test statistic (U) with the z value (z_crit) from the standard Normal Distribution. If there is a statistically significant trend, the parameters of the model (Lambda_hat and Beta_hat) are calculated. By default the results are printed and a plot of the failure interarrival times and MTBF is plotted.

.. admonition:: API Reference

   For inputs and outputs see the `API reference <https://reliability.readthedocs.io/en/latest/API/Repairable_systems/ROCOF.html>`_.

In the example below, we provide the failure interarrival times. The function will run the Laplace test using the default 95% confidence interval and then, when a trend is found, it will plot the MTBF based on the calculated NHPP Power Law model. MTBF = 1/ROCOF. This example is based on Example 5.11 (p275) from Reliability Engineering and Risk analysis listed in the `recommended resources <https://reliability.readthedocs.io/en/latest/Recommended%20resources.html>`_.

.. code:: python

   from reliability.Repairable_systems import ROCOF
   import matplotlib.pyplot as plt
   t = [104,131,1597,59,4,503,157,6,118,173,114,62,101,216,106,140,1,102,3,393,96,232,89,61,37,293,7,165,87,99]
   ROCOF(times_between_failures=t)
   plt.show()

   '''
   Results from ROCOF analysis:
   Laplace test results: U = 2.409, z_crit = (-1.96,+1.96)
   At 95% confidence level the ROCOF is WORSENING. Assume NHPP.
   ROCOF assuming NHPP has parameters: Beta_hat = 1.588 , Lambda_hat = 3.703e-05
   '''
    
.. image:: images/ROCOF.png