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 [https://help.reliasoft.com/reference/reliability_growth_and_repairable_system_analysis Reliability growth reference]''.
</noinclude>
</noinclude>


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*Configuration 4 experienced 4 failures.
*Configuration 4 experienced 4 failures.


 
Do the following:
The objectives are:
#Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimation.
:1) Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimation.
#Estimate the unreliability and reliability by configuration.
:2) Estimate the unreliability and reliability by configuration.
 


'''Solution'''
'''Solution'''
 
<ol>
: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>.
<li>The parameter estimates for the Crow-AMSAA model using the [[Crow-AMSAA (NHPP)#Parameter_Estimation_for_Discrete Data|parameter estimation for discrete data]] methodology yields <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.
</li>
 
<li>The following table displays the results for probability of failure and reliability, and these results are displayed in the next two plots.


<center>'''Estimated Failure Probability and Reliability by Configuration'''</center>
<center>'''Estimated Failure Probability and Reliability by Configuration'''</center>
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[[Image:rga5.16.png|center|450px]]


[[Image:rga5.16.png|center|400px|Estimated unreliability by configuration.]]
[[Image:rga5.17.png|center|450px]]
 
</li>
 
</ol>
[[Image:rga5.17.png|center|400px|Estimated reliability by configuration.]]

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This example appears in the Reliability growth reference.


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.

Do the following:

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

Solution

  1. The parameter estimates for the Crow-AMSAA model using the parameter estimation for discrete data methodology yields [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
    Rga5.16.png
    Rga5.17.png
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