Crow-AMSAA Discrete Model Example: Difference between revisions

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<noinclude>{{Banner RGA Examples}}
<noinclude>{{Banner RGA Examples}}
''This example appears in the [[Crow-AMSAA_-_NHPP|Reliability Growth and Repairable System Analysis Reference book]]''.
''This example appears in the [[Crow-AMSAA (NHPP)|Reliability Growth and Repairable System Analysis Reference book]]''.
</noinclude>
</noinclude>


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'''Solution'''
'''Solution'''


:1) The solution from the [[Crow-AMSAA_-_NHPP#Maximum_Likelihood_Estimators_for_Discrete_Model|MLE equations for discrete models]] yield <math>\lambda = 0.5954\,\!</math> and <math>\beta =0.7801\,\!</math>.
:1) The solution from the [[Crow-AMSAA (NHPP)#Maximum_Likelihood_Estimators_for_Discrete_Model|MLE equations for discrete models]] yield <math>\lambda = 0.5954\,\!</math> and <math>\beta =0.7801\,\!</math>.
:2) The following table displays the results for probability of failure and reliability, and these results are displayed in the next two plots.
:2) The following table displays the results for probability of failure and reliability, and these results are displayed in the next two plots.



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This example appears in the Reliability Growth and Repairable System Analysis Reference book.


A one-shot system underwent reliability growth development testing for a total of 68 trials. Delayed corrective actions were incorporated after the 14th, 33rd and 48th trials. From trial 49 to trial 68, the configuration was not changed.

  • Configuration 1 experienced 5 failures,
  • Configuration 2 experienced 3 failures,
  • Configuration 3 experienced 4 failures and
  • Configuration 4 experienced 4 failures.


The objectives are:

1) Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimation.
2) Estimate the unreliability and reliability by configuration.


Solution

1) The solution from the MLE equations for discrete models yield [math]\displaystyle{ \lambda = 0.5954\,\! }[/math] and [math]\displaystyle{ \beta =0.7801\,\! }[/math].
2) The following table displays the results for probability of failure and reliability, and these results are displayed in the next two plots.


Estimated Failure Probability and Reliability by Configuration
Configuration([math]\displaystyle{ i\,\! }[/math]) Estimated Failure Probability Estimated Reliability
1 0.333 0.667
2 0.234 0.766
3 0.206 0.794
4 0.190 0.810


Estimated unreliability by configuration.


Estimated reliability by configuration.