Mixed Data - Crow-AMSAA Example - Revision history

Lisa Hacker at 21:21, 18 September 2023

2023-09-18T21:21:50Z

← Older revision		Revision as of 21:21, 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 18:36, 30 May 2014

2014-05-30T18:36:57Z

← Older revision		Revision as of 18:36, 30 May 2014
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	<li>The next figure shows the parameters estimated using RGA.		<li>The next figure shows the parameters estimated using RGA.

	[[Image:rga5.32.png\|center\|~~400px\|Estimated parameters of the Crow-AMSAA model.~~]]		[[Image:rga5.32.png\|center\|600px]]
	</li>		</li>
	<li>The figure below shows the calculation of the instantaneous reliability with the 2-sided 90% confidence bounds. From the QCP, it is estimated that the instantaneous reliability at stage 50 (or at the end of the test) is 72.70% with an upper and lower 2-sided 90% confidence bound of 82.36% and 39.59%, respectively.		<li>The figure below shows the calculation of the instantaneous reliability with the 2-sided 90% confidence bounds. From the QCP, it is estimated that the instantaneous reliability at stage 50 (or at the end of the test) is 72.70% with an upper and lower 2-sided 90% confidence bound of 82.36% and 39.59%, respectively.

	[[Image:rga5.33.png\|center\|~~400px\|Instantaneous reliability with 2-sided 90% confidence bounds.~~]]		[[Image:rga5.33.png\|center\|450px]]
	</li>		</li>
	<li>The following plot shows the cumulative reliability with the 2-sided 90% confidence bounds.		<li>The following plot shows the cumulative reliability with the 2-sided 90% confidence bounds.

	[[Image:rga5.34.png\|center\|~~400px\|Plot of cumulative reliability with 2-sided 90% confidence bounds.~~]]		[[Image:rga5.34.png\|center\|450px]]
	</li>		</li>
	<li>The last figure shows the calculation of the expected number of failures after 75 trials. From the QCP, it is estimated that the cumulative number of failures after 75 trials is <math>26.3770\approx 27\,\!</math>. Since 20 failures occurred in the first 50 trials, the estimated number of additional failures is 7.		<li>The last figure shows the calculation of the expected number of failures after 75 trials. From the QCP, it is estimated that the cumulative number of failures after 75 trials is <math>26.3770\approx 27\,\!</math>. Since 20 failures occurred in the first 50 trials, the estimated number of additional failures is 7.

	[[Image:rga5.35.png\|center\|~~400px\|Cumulative number of failures after 75 trials.~~]]		[[Image:rga5.35.png\|center\|450px]]
	</li>		</li>
	</ol>		</ol>

Chris Kahn: moved Mixed Data - Crow AMSAA Example to Mixed Data - Crow-AMSAA Example

2014-05-07T18:49:20Z

moved Mixed Data - Crow AMSAA Example to Mixed Data - Crow-AMSAA Example

← Older revision	Revision as of 18:49, 7 May 2014
(No difference)

David J. Groebel at 00:14, 23 April 2014

2014-04-23T00:14:52Z

← Older revision		Revision as of 00:14, 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>

Chris Kahn at 23:30, 31 January 2014

2014-01-31T23:30:55Z

← Older revision		Revision as of 23:30, 31 January 2014
Line 5:		Line 5:
	A one-shot system underwent reliability growth development for a total of 50 trials. The test was performed as a combination of configuration in groups and individual trial by trial. The table below shows the data set obtained from the test. The first column specifies the number of failures that occurred in each interval, and the second column shows the cumulative number of trials in that interval. Do the following:		A one-shot system underwent reliability growth development for a total of 50 trials. The test was performed as a combination of configuration in groups and individual trial by trial. The table below shows the data set obtained from the test. The first column specifies the number of failures that occurred in each interval, and the second column shows the cumulative number of trials in that interval. Do the following:

	1) Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimators.		#Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimators.
			#What are the instantaneous reliability and the 2-sided 90% confidence bounds at the end of the test?
	2) What are the instantaneous reliability and the 2-sided 90% confidence bounds at the end of the test?		#Plot the cumulative reliability with 2-sided 90% confidence bounds.
			#If the test was continued for another 25 trials what would the expected number of additional failures be?
	3) Plot the cumulative reliability with 2-sided 90% confidence bounds.

	4) If the test was continued for another 25 trials what would the expected number of additional failures be?

	<center>'''Mixed Data'''</center>		<center>'''Mixed Data'''</center>
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	'''Solution'''		'''Solution'''
			<ol>
	1) The next figure shows the parameters estimated using RGA.		<li>The next figure shows the parameters estimated using RGA.

	[[Image:rga5.32.png\|center\|400px\|Estimated parameters of the Crow-AMSAA model.]]		[[Image:rga5.32.png\|center\|400px\|Estimated parameters of the Crow-AMSAA model.]]
			</li>
	2) The figure below shows the calculation of the instantaneous reliability with the 2-sided 90% confidence bounds. From the QCP, it is estimated that the instantaneous reliability at stage 50 (or at the end of the test) is 72.70% with an upper and lower 2-sided 90% confidence bound of 82.36% and 39.59%, respectively.		<li>The figure below shows the calculation of the instantaneous reliability with the 2-sided 90% confidence bounds. From the QCP, it is estimated that the instantaneous reliability at stage 50 (or at the end of the test) is 72.70% with an upper and lower 2-sided 90% confidence bound of 82.36% and 39.59%, respectively.

	[[Image:rga5.33.png\|center\|400px\|Instantaneous reliability with 2-sided 90% confidence bounds.]]		[[Image:rga5.33.png\|center\|400px\|Instantaneous reliability with 2-sided 90% confidence bounds.]]
			</li>
	3) The following plot shows the cumulative reliability with the 2-sided 90% confidence bounds.		<li>The following plot shows the cumulative reliability with the 2-sided 90% confidence bounds.

	[[Image:rga5.34.png\|center\|400px\|Plot of cumulative reliability with 2-sided 90% confidence bounds.]]		[[Image:rga5.34.png\|center\|400px\|Plot of cumulative reliability with 2-sided 90% confidence bounds.]]
			</li>
	4) The last figure shows the calculation of the expected number of failures after 75 trials. From the QCP, it is estimated that the cumulative number of failures after 75 trials is <math>26.3770\approx 27\,\!</math>. Since 20 failures occurred in the first 50 trials, the estimated number of additional failures is 7.		<li>The last figure shows the calculation of the expected number of failures after 75 trials. From the QCP, it is estimated that the cumulative number of failures after 75 trials is <math>26.3770\approx 27\,\!</math>. Since 20 failures occurred in the first 50 trials, the estimated number of additional failures is 7.

	[[Image:rga5.35.png\|center\|400px\|Cumulative number of failures after 75 trials.]]		[[Image:rga5.35.png\|center\|400px\|Cumulative number of failures after 75 trials.]]
			</li>
			</ol>

David J. Groebel at 17:45, 27 January 2014

2014-01-27T17:45:50Z

← Older revision		Revision as of 17:45, 27 January 2014
Line 6:		Line 6:

	1) Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimators.		1) Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimators.

	2) What are the instantaneous reliability and the 2-sided 90% confidence bounds at the end of the test?		2) What are the instantaneous reliability and the 2-sided 90% confidence bounds at the end of the test?

	3) Plot the cumulative reliability with 2-sided 90% confidence bounds.		3) Plot the cumulative reliability with 2-sided 90% confidence bounds.

	4) If the test was continued for another 25 trials what would the expected number of additional failures be?		4) If the test was continued for another 25 trials what would the expected number of additional failures be?

David J. Groebel at 17:45, 27 January 2014

2014-01-27T17:45:27Z

← Older revision		Revision as of 17:45, 27 January 2014
Line 5:		Line 5:
	A one-shot system underwent reliability growth development for a total of 50 trials. The test was performed as a combination of configuration in groups and individual trial by trial. The table below shows the data set obtained from the test. The first column specifies the number of failures that occurred in each interval, and the second column shows the cumulative number of trials in that interval. Do the following:		A one-shot system underwent reliability growth development for a total of 50 trials. The test was performed as a combination of configuration in groups and individual trial by trial. The table below shows the data set obtained from the test. The first column specifies the number of failures that occurred in each interval, and the second column shows the cumulative number of trials in that interval. Do the following:

	:1) Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimators.		1) Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimators.
	:2) What are the instantaneous reliability and the 2-sided 90% confidence bounds at the end of the test?		2) What are the instantaneous reliability and the 2-sided 90% confidence bounds at the end of the test?
	:3) Plot the cumulative reliability with 2-sided 90% confidence bounds.		3) Plot the cumulative reliability with 2-sided 90% confidence bounds.
	:4) If the test was continued for another 25 trials what would the expected number of additional failures be?		4) If the test was continued for another 25 trials what would the expected number of additional failures be?

	<center>'''Mixed Data'''</center>		<center>'''Mixed Data'''</center>

David J. Groebel at 17:45, 27 January 2014

2014-01-27T17:45:05Z

← Older revision		Revision as of 17:45, 27 January 2014
Line 9:		Line 9:
	:3) Plot the cumulative reliability with 2-sided 90% confidence bounds.		:3) Plot the cumulative reliability with 2-sided 90% confidence bounds.
	:4) If the test was continued for another 25 trials what would the expected number of additional failures be?		:4) If the test was continued for another 25 trials what would the expected number of additional failures be?


	<center>'''Mixed Data'''</center>		<center>'''Mixed Data'''</center>
Line 41:		Line 40:
	'''Solution'''		'''Solution'''

	:1) The next figure shows the parameters estimated using RGA.		1) The next figure shows the parameters estimated using RGA.

	[[Image:rga5.32.png\|center\|400px\|Estimated parameters of the Crow-AMSAA model.]]		[[Image:rga5.32.png\|center\|400px\|Estimated parameters of the Crow-AMSAA model.]]

			2) The figure below shows the calculation of the instantaneous reliability with the 2-sided 90% confidence bounds. From the QCP, it is estimated that the instantaneous reliability at stage 50 (or at the end of the test) is 72.70% with an upper and lower 2-sided 90% confidence bound of 82.36% and 39.59%, respectively.
	:2) The figure below shows the calculation of the instantaneous reliability with the 2-sided 90% confidence bounds. From the QCP, it is estimated that the instantaneous reliability at stage 50 (or at the end of the test) is 72.70% with an upper and lower 2-sided 90% confidence bound of 82.36% and 39.59%, respectively.

	[[Image:rga5.33.png\|center\|400px\|Instantaneous reliability with 2-sided 90% confidence bounds.]]		[[Image:rga5.33.png\|center\|400px\|Instantaneous reliability with 2-sided 90% confidence bounds.]]

			3) The following plot shows the cumulative reliability with the 2-sided 90% confidence bounds.
	:3) The following plot shows the cumulative reliability with the 2-sided 90% confidence bounds.

	[[Image:rga5.34.png\|center\|400px\|Plot of cumulative reliability with 2-sided 90% confidence bounds.]]		[[Image:rga5.34.png\|center\|400px\|Plot of cumulative reliability with 2-sided 90% confidence bounds.]]

			4) The last figure shows the calculation of the expected number of failures after 75 trials. From the QCP, it is estimated that the cumulative number of failures after 75 trials is <math>26.3770\approx 27\,\!</math>. Since 20 failures occurred in the first 50 trials, the estimated number of additional failures is 7.
	:4) The last figure shows the calculation of the expected number of failures after 75 trials. From the QCP, it is estimated that the cumulative number of failures after 75 trials is <math>26.3770\approx 27\,\!</math>. Since 20 failures occurred in the first 50 trials, the estimated number of additional failures is 7.

	[[Image:rga5.35.png\|center\|400px\|Cumulative number of failures after 75 trials.]]		[[Image:rga5.35.png\|center\|400px\|Cumulative number of failures after 75 trials.]]

Chris Kahn at 23:53, 24 January 2014

2014-01-24T23:53:12Z

← Older revision		Revision as of 23:53, 24 January 2014
Line 48:		Line 48:
	:2) The figure below shows the calculation of the instantaneous reliability with the 2-sided 90% confidence bounds. From the QCP, it is estimated that the instantaneous reliability at stage 50 (or at the end of the test) is 72.70% with an upper and lower 2-sided 90% confidence bound of 82.36% and 39.59%, respectively.		:2) The figure below shows the calculation of the instantaneous reliability with the 2-sided 90% confidence bounds. From the QCP, it is estimated that the instantaneous reliability at stage 50 (or at the end of the test) is 72.70% with an upper and lower 2-sided 90% confidence bound of 82.36% and 39.59%, respectively.

	[[Image:rga5.33.png\|center\|~~300px~~\|Instantaneous reliability with 2-sided 90% confidence bounds.]]		[[Image:rga5.33.png\|center\|400px\|Instantaneous reliability with 2-sided 90% confidence bounds.]]


	:3) The following plot shows the cumulative reliability with the 2-sided 90% confidence bounds.		:3) The following plot shows the cumulative reliability with the 2-sided 90% confidence bounds.

	[[Image:rga5.34.png\|center\|~~300px~~\|Plot of cumulative reliability with 2-sided 90% confidence bounds.]]		[[Image:rga5.34.png\|center\|400px\|Plot of cumulative reliability with 2-sided 90% confidence bounds.]]


	:4) The last figure shows the calculation of the expected number of failures after 75 trials. From the QCP, it is estimated that the cumulative number of failures after 75 trials is <math>26.3770\approx 27\,\!</math>. Since 20 failures occurred in the first 50 trials, the estimated number of additional failures is 7.		:4) The last figure shows the calculation of the expected number of failures after 75 trials. From the QCP, it is estimated that the cumulative number of failures after 75 trials is <math>26.3770\approx 27\,\!</math>. Since 20 failures occurred in the first 50 trials, the estimated number of additional failures is 7.

	[[Image:rga5.35.png\|center\|~~300px~~\|Cumulative number of failures after 75 trials.]]		[[Image:rga5.35.png\|center\|400px\|Cumulative number of failures after 75 trials.]]

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

2014-01-20T18:37:53Z

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 for a total of 50 trials. The test was performed as a combination of configuration in groups and individual trial by trial. The table below shows the data set obtained from the test. The first column specifies the number of failures that occurred in each interval, and the second column shows the cumulative number of trials in that interval. Do the following:

:1) Estimate the parameters of the Crow-AMSAA model using maximum likelihood estimators.
:2) What are the instantaneous reliability and the 2-sided 90% confidence bounds at the end of the test?
:3) Plot the cumulative reliability with 2-sided 90% confidence bounds.
:4) If the test was continued for another 25 trials what would the expected number of additional failures be?

<center>'''Mixed Data'''</center>
{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
!Failures in Interval
!Cumulative Trials
!Failures in Interval
!Cumulative Trials
|-
|3|| 4|| 1|| 25
|-
|0|| 5|| 1|| 28
|-
|4|| 9|| 0|| 32
|-
|1|| 12|| 2|| 37
|-
|0|| 13|| 0|| 39
|-
|1|| 15|| 1|| 40
|-
|2|| 19|| 1|| 44
|-
|1|| 20|| 0|| 46
|-
|1|| 22|| 1|| 49
|-
|0|| 24|| 0|| 50
|}

'''Solution'''

:1) The next figure shows the parameters estimated using RGA.

[[Image:rga5.32.png|center|400px|Estimated parameters of the Crow-AMSAA model.]]

:2) The figure below shows the calculation of the instantaneous reliability with the 2-sided 90% confidence bounds. From the QCP, it is estimated that the instantaneous reliability at stage 50 (or at the end of the test) is 72.70% with an upper and lower 2-sided 90% confidence bound of 82.36% and 39.59%, respectively.

[[Image:rga5.33.png|center|300px|Instantaneous reliability with 2-sided 90% confidence bounds.]]

:3) The following plot shows the cumulative reliability with the 2-sided 90% confidence bounds.

[[Image:rga5.34.png|center|300px|Plot of cumulative reliability with 2-sided 90% confidence bounds.]]

:4) The last figure shows the calculation of the expected number of failures after 75 trials. From the QCP, it is estimated that the cumulative number of failures after 75 trials is <math>26.3770\approx 27\,\!</math>. Since 20 failures occurred in the first 50 trials, the estimated number of additional failures is 7.

[[Image:rga5.35.png|center|300px|Cumulative number of failures after 75 trials.]]