Crow Extended Model Fleet Analysis Example - Revision history

Lisa Hacker at 20:54, 18 September 2023

2023-09-18T20:54:39Z

← Older revision		Revision as of 20:54, 18 September 2023
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [~~[Fleet_Data_Analysis\|~~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>

Chris Kahn at 16:16, 12 June 2014

2014-06-12T16:16:25Z

← Older revision		Revision as of 16:16, 12 June 2014
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	{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"		{\|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|-		\|-
	\|colspan="2" style="text-align:center"\|'''Fleet ~~data~~'''		\|colspan="2" style="text-align:center"\|'''Fleet Data'''
	\|-		\|-
	!System		!System

David J. Groebel at 20:07, 2 June 2014

2014-06-02T20:07:52Z

← Older revision		Revision as of 20:07, 2 June 2014
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [[Fleet_Data_Analysis\|Reliability Growth and Repairable System Analysis Reference ~~book~~]]''.		''This example appears in the [[Fleet_Data_Analysis\|Reliability Growth and Repairable System Analysis Reference]]''.
	</noinclude>		</noinclude>

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	<li>The next figure shows the estimated Crow Extended parameters.		<li>The next figure shows the estimated Crow Extended parameters.

	[[Image:rga13.8.png~~\|thumb~~\|center\|~~400px\|Estimated Crow Extended parameters.~~]]		[[Image:rga13.8.png\|center\|600px]]
	</li>		</li>
	<li>Upon observing the estimated parameter <math>\beta \,\!</math>, it does appear that the systems were randomly ordered since <math>\beta =0.8569\,\!</math>. This value is close to 1. You can also verify that the confidence bounds on <math>\beta \,\!</math> include 1 by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine graphically if the systems were randomly ordered by using the System Operation plot as shown below. Looking at the Cum. Time Line, it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered.		<li>Upon observing the estimated parameter <math>\beta \,\!</math>, it does appear that the systems were randomly ordered since <math>\beta =0.8569\,\!</math>. This value is close to 1. You can also verify that the confidence bounds on <math>\beta \,\!</math> include 1 by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine graphically if the systems were randomly ordered by using the System Operation plot as shown below. Looking at the Cum. Time Line, it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered.

	[[Image:rga13.9.png~~\|thumb~~\|center\|~~400px\|System Operation plot.~~]]		[[Image:rga13.9.png\|center\|450px]]
	</li>		</li>
	<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.		<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.
	[[Image:FleetExampleGPPlot.png~~\|thumb~~\|center\|450px~~\|Growth Potential MTBF Plot.~~]]		[[Image:FleetExampleGPPlot.png\|center\|450px]]

	To estimate the number of failures during the next 4,000 hours, calculate the following:		To estimate the number of failures during the next 4,000 hours, calculate the following:

David J. Groebel at 23:05, 22 April 2014

2014-04-22T23:05:15Z

← Older revision		Revision as of 23:05, 22 April 2014
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	<li>The next figure shows the estimated Crow Extended parameters.		<li>The next figure shows the estimated Crow Extended parameters.

	[[Image:rga13.8.png\|thumb\|center\|~~450px~~\|Estimated Crow Extended parameters.]]		[[Image:rga13.8.png\|thumb\|center\|400px\|Estimated Crow Extended parameters.]]
	</li>		</li>
	<li>Upon observing the estimated parameter <math>\beta \,\!</math>, it does appear that the systems were randomly ordered since <math>\beta =0.8569\,\!</math>. This value is close to 1. You can also verify that the confidence bounds on <math>\beta \,\!</math> include 1 by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine graphically if the systems were randomly ordered by using the System Operation plot as shown below. Looking at the Cum. Time Line, it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered.		<li>Upon observing the estimated parameter <math>\beta \,\!</math>, it does appear that the systems were randomly ordered since <math>\beta =0.8569\,\!</math>. This value is close to 1. You can also verify that the confidence bounds on <math>\beta \,\!</math> include 1 by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine graphically if the systems were randomly ordered by using the System Operation plot as shown below. Looking at the Cum. Time Line, it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered.

	[[Image:rga13.9.png\|thumb\|center\|~~450px~~\|System Operation plot.]]		[[Image:rga13.9.png\|thumb\|center\|400px\|System Operation plot.]]
	</li>		</li>
	<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.		<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.

David J. Groebel at 19:51, 6 February 2014

2014-02-06T19:51:32Z

← Older revision		Revision as of 19:51, 6 February 2014
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	<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.		<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.
	[[Image:FleetExampleGPPlot.png\|thumb\|center\|450px\|Growth Potential MTBF Plot.]]		[[Image:FleetExampleGPPlot.png\|thumb\|center\|450px\|Growth Potential MTBF Plot.]]
			To estimate the number of failures during the next 4,000 hours, calculate the following:

			<math>\begin{align}
			N=& \frac{4000}{1035.6802}\\
			= & 3.8622\end{align}\,\!</math>

			Therefore, it is estimated that <math>\approx\,\!</math> 4 failures will be observed during the next 4,000 hours of fleet operation.
	</li>		</li>
	</ol>		</ol>

David J. Groebel at 19:43, 6 February 2014

2014-02-06T19:43:42Z

← Older revision		Revision as of 19:43, 6 February 2014
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	</li>		</li>
	<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.		<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.
	[[~~File~~:FleetExampleGPPlot.png]]		[[Image:FleetExampleGPPlot.png\|thumb\|center\|450px\|Growth Potential MTBF Plot.]]
	</li>		</li>
	</ol>		</ol>

David J. Groebel at 19:42, 6 February 2014

2014-02-06T19:42:12Z

← Older revision		Revision as of 19:42, 6 February 2014
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	[[Image:rga13.9.png\|thumb\|center\|450px\|System Operation plot.]]		[[Image:rga13.9.png\|thumb\|center\|450px\|System Operation plot.]]
			</li>
			<li> After implementing the delayed fixes, the system's projected MTBF is equal to <math>1035.6802\,\!</math> as shown in the plot below.
			[[File:FleetExampleGPPlot.png]]
	</li>		</li>
	</ol>		</ol>

Chris Kahn at 18:27, 6 February 2014

2014-02-06T18:27:44Z

← Older revision		Revision as of 18:27, 6 February 2014
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	11 systems from the field were chosen for fleet analysis. Each system had at least one failure. All of the systems had a start time equal to zero and the last failure for each system corresponds to the end time. Group the data based on a fixed interval of 3,000 hours, and assume a fixed effectiveness factor equal to 0.4. Do the following:		11 systems from the field were chosen for fleet analysis. Each system had at least one failure. All of the systems had a start time equal to zero and the last failure for each system corresponds to the end time. Group the data based on a fixed interval of 3,000 hours, and assume a fixed effectiveness factor equal to 0.4. Do the following:

	1) Estimate the parameters of the Crow Extended model.		#Estimate the parameters of the Crow Extended model.
			#Based on the analysis, does it appear that the systems were randomly ordered?
	2) Based on the analysis, does it appear that the systems were randomly ordered?		#After the implementation of the delayed fixes, how many failures would you expect within the next 4,000 hours of fleet operation.

	3) After the implementation of the delayed fixes, how many failures would you expect within the next 4,000 hours of fleet operation.

	{\|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'''
	<br>		<ol>
	~~:1)~~ The next figure shows the estimated Crow Extended parameters.		<li>The next figure shows the estimated Crow Extended parameters.

	[[Image:rga13.8.png\|thumb\|center\|450px\|Estimated Crow Extended parameters.]]		[[Image:rga13.8.png\|thumb\|center\|450px\|Estimated Crow Extended parameters.]]
			</li>
	~~:2)~~ Upon observing the estimated parameter <math>\beta \,\!</math>, it does appear that the systems were randomly ordered since <math>\beta =0.8569\,\!</math>. This value is close to 1. You can also verify that the confidence bounds on <math>\beta \,\!</math> include 1 by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine graphically if the systems were randomly ordered by using the System Operation plot as shown below. Looking at the Cum. Time Line, it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered.		<li>Upon observing the estimated parameter <math>\beta \,\!</math>, it does appear that the systems were randomly ordered since <math>\beta =0.8569\,\!</math>. This value is close to 1. You can also verify that the confidence bounds on <math>\beta \,\!</math> include 1 by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine graphically if the systems were randomly ordered by using the System Operation plot as shown below. Looking at the Cum. Time Line, it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered.

	[[Image:rga13.9.png\|thumb\|center\|450px\|System Operation plot.]]		[[Image:rga13.9.png\|thumb\|center\|450px\|System Operation plot.]]
			</li>
			</ol>

Kate Racaza at 18:38, 4 February 2014

2014-02-04T18:38:08Z

← Older revision		Revision as of 18:38, 4 February 2014
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	<noinclude>{{Banner RGA Examples~~}}{{Navigation box~~}}		<noinclude>{{Banner RGA Examples}}
	''~~These examples appear~~ in the [[Fleet_Data_Analysis\|Reliability Growth and Repairable System Analysis Reference book]]''.		''This example appears in the [[Fleet_Data_Analysis\|Reliability Growth and Repairable System Analysis Reference book]]''.
	</noinclude>		</noinclude>


	11 systems from the field were chosen for fleet analysis. Each system had at least one failure. All of the systems had a start time equal to zero and the last failure for each system corresponds to the end time. Group the data based on a fixed interval of 3,000 hours, and assume a fixed effectiveness factor equal to 0.4. Do the following:		11 systems from the field were chosen for fleet analysis. Each system had at least one failure. All of the systems had a start time equal to zero and the last failure for each system corresponds to the end time. Group the data based on a fixed interval of 3,000 hours, and assume a fixed effectiveness factor equal to 0.4. Do the following:

Kate Racaza: Created page with '{{Banner RGA Examples}}{{Navigation box}} ''These examples appear in the Reliability Growth and Repairable System Analysis Reference book''.
2014-01-29T19:16:56Z

Created page with '<noinclude>{{Banner RGA Examples}}{{Navigation box}} ''These examples appear in the Reliability Growth and Repairable System Analysis Reference book''. </…'

New page
<noinclude>{{Banner RGA Examples}}{{Navigation box}}
''These examples appear in the [[Fleet_Data_Analysis|Reliability Growth and Repairable System Analysis Reference book]]''.
</noinclude>

11 systems from the field were chosen for fleet analysis. Each system had at least one failure. All of the systems had a start time equal to zero and the last failure for each system corresponds to the end time. Group the data based on a fixed interval of 3,000 hours, and assume a fixed effectiveness factor equal to 0.4. Do the following:

1) Estimate the parameters of the Crow Extended model.

2) Based on the analysis, does it appear that the systems were randomly ordered?

3) After the implementation of the delayed fixes, how many failures would you expect within the next 4,000 hours of fleet operation.

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="2" style="text-align:center"|'''Fleet data'''
|-
!System
!Times-to-Failure
|-
|1|| 1137 BD1, 1268 BD2
|-
|2|| 682 BD3, 744 A, 1336 BD1
|-
|3|| 95 BD1, 1593 BD3
|-
|4|| 1421 A
|-
|5|| 1091 A, 1574 BD2
|-
|6|| 1415 BD4
|-
|7|| 598 BD4, 1290 BD1
|-
|8|| 1556 BD5
|-
|9|| 55 BD4
|-
|10|| 730 BD1, 1124 BD3
|-
|11|| 1400 BD4, 1568 A
|}

'''Solution'''
<br>
:1) The next figure shows the estimated Crow Extended parameters.

[[Image:rga13.8.png|thumb|center|450px|Estimated Crow Extended parameters.]]

:2) Upon observing the estimated parameter <math>\beta \,\!</math>, it does appear that the systems were randomly ordered since <math>\beta =0.8569\,\!</math>. This value is close to 1. You can also verify that the confidence bounds on <math>\beta \,\!</math> include 1 by going to the QCP and calculating the parameter bounds or by viewing the Beta Bounds plot. However, you can also determine graphically if the systems were randomly ordered by using the System Operation plot as shown below. Looking at the Cum. Time Line, it does not appear that the failures have a trend associated with them. Therefore, the systems can be assumed to be randomly ordered.

[[Image:rga13.9.png|thumb|center|450px|System Operation plot.]]