Grouped per Configuration - Lloyd-Lipow Model - Revision history

Lisa Hacker at 21:22, 18 September 2023

2023-09-18T21:22:53Z

← Older revision		Revision as of 21:22, 18 September 2023
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [~~[Lloyd-Lipow\|~~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 19:43, 29 May 2014

2014-05-29T19:43:34Z

← Older revision		Revision as of 19:43, 29 May 2014
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [[Lloyd-Lipow\|Reliability Growth and Repairable System Analysis Reference ~~book~~]]''.		''This example appears in the [[Lloyd-Lipow\|Reliability Growth and Repairable System Analysis Reference]]''.
	</noinclude>		</noinclude>

David J. Groebel at 19:42, 29 May 2014

2014-05-29T19:42:19Z

← Older revision		Revision as of 19:42, 29 May 2014
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	\|15\|\| 14\|\| 12		\|15\|\| 14\|\| 12
	\|}		\|}


	'''Solution'''		'''Solution'''
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	<li>The figure below displays the entered data and the estimated Lloyd-Lipow parameters.		<li>The figure below displays the entered data and the estimated Lloyd-Lipow parameters.

	[[Image:rga6.4.png~~\|thumb~~\|center\|~~400px\|Estimated Lloyd-Lipow parameters using MLE.~~]]		[[Image:rga6.4.png\|center\|600px]]
	</li>		</li>
	<li>The maximum achievable reliability as the number of test stages approaches infinity is equal to the value of <math>R\,\!</math>. Therefore, <math>R=0.7157\,\!</math>.		<li>The maximum achievable reliability as the number of test stages approaches infinity is equal to the value of <math>R\,\!</math>. Therefore, <math>R=0.7157\,\!</math>.
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	<li>The maximum achievable reliability with a 90% confidence level can be estimated by viewing the confidence bounds on the parameters in the QCP, as shown in the figure below. The lower bound on the value of <math>R\,\!</math> is equal to 0.6691 .		<li>The maximum achievable reliability with a 90% confidence level can be estimated by viewing the confidence bounds on the parameters in the QCP, as shown in the figure below. The lower bound on the value of <math>R\,\!</math> is equal to 0.6691 .

	[[Image:rga6.5.png~~\|thumb~~\|center\|~~400px\|Confidence bounds on the parameters.~~]]</li>		[[Image:rga6.5.png\|center\|450px]]</li>
	</ol>		</ol>

Chris Kahn at 23:32, 31 January 2014

2014-01-31T23:32:18Z

← Older revision		Revision as of 23:32, 31 January 2014
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	A 15-stage reliability development test program was performed. The grouped per configuration data set is shown in the following table. Do the following:		A 15-stage reliability development test program was performed. The grouped per configuration data set is shown in the following table. Do the following:

	~~:1)~~ Fit the Lloyd-Lipow model to the data using MLE.		#Fit the Lloyd-Lipow model to the data using MLE.
	~~:2)~~ What is the maximum reliability attained as the number of test stages approaches infinity?		#What is the maximum reliability attained as the number of test stages approaches infinity?
	~~:3)~~ What is the maximum achievable reliability with a 90% confidence level?		#What is the maximum achievable reliability with a 90% confidence level?

	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
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	'''Solution'''		'''Solution'''

	~~:1)~~ The figure below displays the entered data and the estimated Lloyd-Lipow parameters.		<ol>
			<li>The figure below displays the entered data and the estimated Lloyd-Lipow parameters.

	[[Image:rga6.4.png\|thumb\|center\|400px\|Estimated Lloyd-Lipow parameters using MLE.]]		[[Image:rga6.4.png\|thumb\|center\|400px\|Estimated Lloyd-Lipow parameters using MLE.]]
			</li>
	~~:2)~~ The maximum achievable reliability as the number of test stages approaches infinity is equal to the value of <math>R\,\!</math>. Therefore, <math>R=0.7157\,\!</math>.		<li>The maximum achievable reliability as the number of test stages approaches infinity is equal to the value of <math>R\,\!</math>. Therefore, <math>R=0.7157\,\!</math>.
	~~:3)~~ The maximum achievable reliability with a 90% confidence level can be estimated by viewing the confidence bounds on the parameters in the QCP, as shown in the figure below. The lower bound on the value of <math>R\,\!</math> is equal to 0.6691 .		</li>
			<li>The maximum achievable reliability with a 90% confidence level can be estimated by viewing the confidence bounds on the parameters in the QCP, as shown in the figure below. The lower bound on the value of <math>R\,\!</math> is equal to 0.6691 .

	[[Image:rga6.5.png\|thumb\|center\|400px\|Confidence bounds on the parameters.]]		[[Image:rga6.5.png\|thumb\|center\|400px\|Confidence bounds on the parameters.]]</li>
			</ol>

Kate Racaza: Created page with '{{Banner RGA Examples}} ''This example appears in the Reliability Growth and Repairable System Analysis Reference book''. A 15-stage reli…'

2014-01-21T19:00:40Z

Created page with '<noinclude>{{Banner RGA Examples}} ''This example appears in the Reliability Growth and Repairable System Analysis Reference book''. </noinclude> A 15-stage reli…'

New page

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

A 15-stage reliability development test program was performed. The grouped per configuration data set is shown in the following table. Do the following:

:1) Fit the Lloyd-Lipow model to the data using MLE.
:2) What is the maximum reliability attained as the number of test stages approaches infinity?
:3) What is the maximum achievable reliability with a 90% confidence level?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|+'''Grouped per Configuration Data'''
!Stage, <math>k\,\!</math>
!Number of Tests (<math>n_k\,\!</math>)
!Number of Successes (<math>S_k\,\!</math>)
|-
|1|| 10|| 3
|-
|2|| 10|| 3
|-
|3|| 10|| 4
|-
|4|| 10|| 5
|-
|5|| 10|| 5
|-
|6|| 12|| 6
|-
|7|| 12|| 5
|-
|8|| 12|| 7
|-
|9|| 14|| 8
|-
|10|| 14|| 8
|-
|11|| 14|| 10
|-
|12|| 14|| 12
|-
|13|| 14|| 11
|-
|14|| 14|| 12
|-
|15|| 14|| 12
|}

'''Solution'''

:1) The figure below displays the entered data and the estimated Lloyd-Lipow parameters.

[[Image:rga6.4.png|thumb|center|400px|Estimated Lloyd-Lipow parameters using MLE.]]

:2) The maximum achievable reliability as the number of test stages approaches infinity is equal to the value of <math>R\,\!</math>. Therefore, <math>R=0.7157\,\!</math>.
:3) The maximum achievable reliability with a 90% confidence level can be estimated by viewing the confidence bounds on the parameters in the QCP, as shown in the figure below. The lower bound on the value of <math>R\,\!</math> is equal to 0.6691 .

[[Image:rga6.5.png|thumb|center|400px|Confidence bounds on the parameters.]]