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 | ''This example appears in the [[Crow-AMSAA (NHPP)|Reliability Growth and Repairable System Analysis Reference]]''. | ||
</noinclude> | </noinclude> | ||
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*Configuration 4 experienced 4 failures. | *Configuration 4 experienced 4 failures. | ||
Do the following: | |||
#Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimation. | |||
#Estimate the unreliability and reliability by configuration. | |||
'''Solution''' | '''Solution''' | ||
<ol> | |||
<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>. | |||
</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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|4|| 0.190|| 0.810 | |4|| 0.190|| 0.810 | ||
|} | |} | ||
[[Image:rga5.16.png|center|400px|Estimated unreliability by configuration.]] | [[Image:rga5.16.png|center|400px|Estimated unreliability by configuration.]] | ||
[[Image:rga5.17.png|center|400px|Estimated reliability by configuration.]] | [[Image:rga5.17.png|center|400px|Estimated reliability by configuration.]] | ||
</li> | |||
</ol> | |||
Revision as of 00:10, 23 April 2014
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This example appears in the Reliability Growth and Repairable System Analysis 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:
- Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimation.
- Estimate the unreliability and reliability by configuration.
Solution
- 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].
- 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 
