Crow-AMSAA Discrete Model Example - Revision history

Lisa Hacker at 21:16, 18 September 2023

2023-09-18T21:16:41Z

← Older revision		Revision as of 21:16, 18 September 2023
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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 [https://help.reliasoft.com/reference/reliability_growth_and_repairable_system_analysis Reliability growth reference]''.
	</noinclude>		</noinclude>

David J. Groebel at 18:30, 30 May 2014

2014-05-30T18:30:33Z

← Older revision		Revision as of 18:30, 30 May 2014
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	\|}		\|}

	[[Image:rga5.16.png\|center\|~~400px\|Estimated unreliability by configuration.~~]]		[[Image:rga5.16.png\|center\|450px]]

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

David J. Groebel at 00:10, 23 April 2014

2014-04-23T00:10:20Z

← Older revision		Revision as of 00:10, 23 April 2014
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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]]''.
	</noinclude>		</noinclude>

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

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

	'''Solution'''		'''Solution'''
			<ol>
	1) 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>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>
	2) The following table displays the results for probability of failure and reliability, and these results are displayed in the next two plots.		<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>

David J. Groebel at 00:27, 31 January 2014

2014-01-31T00:27:57Z

← Older revision		Revision as of 00:27, 31 January 2014
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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.]]

David J. Groebel at 00:24, 31 January 2014

2014-01-31T00:24:42Z

← Older revision		Revision as of 00:24, 31 January 2014
Line 9:		Line 9:
	*Configuration 3 experienced 4 failures and		*Configuration 3 experienced 4 failures and
	*Configuration 4 experienced 4 failures.		*Configuration 4 experienced 4 failures.


	The objectives are:		The objectives are:
	:1) 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.
	:2) Estimate the unreliability and reliability by configuration.		2) Estimate the unreliability and reliability by configuration.

			'''Solution'''

	~~'''Solution'''~~		1) 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>.

	: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.

	<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.]]

David J. Groebel at 17:43, 27 January 2014

2014-01-27T17:43:16Z

← Older revision		Revision as of 17:43, 27 January 2014
Line 12:		Line 12:

	The objectives are:		The objectives are:
	:1) 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.
	:2) Estimate the unreliability and reliability by configuration.		:2) Estimate the unreliability and reliability by configuration.


	'''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.


	<center>'''Estimated Failure Probability and Reliability by Configuration'''</center>		<center>'''Estimated Failure Probability and Reliability by Configuration'''</center>

Chris Kahn at 21:53, 22 January 2014

2014-01-22T21:53:45Z

← Older revision		Revision as of 21:53, 22 January 2014
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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.

Kate Racaza: Created page with '{{Banner RGA Examples}} ''This example appears in the Reliability Growth and Repairable System Analysis Reference book''. A one-sho…'

2013-11-21T23:25:31Z

Created page with '<noinclude>{{Banner RGA Examples}} ''This example appears in the Reliability Growth and Repairable System Analysis Reference book''. </noinclude> A one-sho…'

New page

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

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 [[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.

<center>'''Estimated Failure Probability and Reliability by Configuration'''</center>
{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
!Configuration(<math>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
|}

[[Image:rga5.16.png|center|400px|Estimated unreliability by configuration.]]

[[Image:rga5.17.png|center|400px|Estimated reliability by configuration.]]