Optimum Overhaul Example - Revision history

Lisa Hacker at 20:54, 18 September 2023

2023-09-18T20:54:29Z

← 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 [~~[Repairable_Systems_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>

David J. Groebel at 16:03, 16 October 2014

2014-10-16T16:03:26Z

← Older revision		Revision as of 16:03, 16 October 2014
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	</li>		</li>
	<li>Since <math>\beta <1\,\!</math> ~~then~~ the systems are ~~not~~ wearing out and it would ~~not~~ be cost-effective to implement an overhaul policy. An overhaul policy makes sense only if the systems are wearing out~~. Otherwise, an overhauled unit would have the same probability of failing as a unit that was not overhauled~~.		<li>Since <math>\beta >1\,\!</math> the systems are wearing out and it would be cost-effective to implement an overhaul policy. An overhaul policy makes sense only if the systems are wearing out.
	</li>		</li>
	</ol>		</ol>

Chris Kahn at 17:47, 12 June 2014

2014-06-12T17:47:15Z

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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="3" style="text-align:center"\|'''Field ~~data~~'''		\|colspan="3" style="text-align:center"\|'''Field Data'''
	\|-		\|-
	!System 1		!System 1

David J. Groebel at 20:01, 2 June 2014

2014-06-02T20:01:48Z

← Older revision		Revision as of 20:01, 2 June 2014
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	<noinclude>{{Banner RGA Examples}}		<noinclude>{{Banner RGA Examples}}
	''This example appears in the [[Repairable_Systems_Analysis\|Reliability Growth and Repairable System Analysis Reference ~~book~~]]''.		''This example appears in the [[Repairable_Systems_Analysis\|Reliability Growth and Repairable System Analysis Reference]]''.
	</noinclude>		</noinclude>

David J. Groebel at 20:01, 2 June 2014

2014-06-02T20:01:07Z

← Older revision		Revision as of 20:01, 2 June 2014
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	<li>The next figure shows the estimated Power Law parameters.		<li>The next figure shows the estimated Power Law parameters.

	[[Image:rga13.12.png~~\|thumb~~\|center\|~~450px\|Entered data and the estimated Power Law parameters.~~]]		[[Image:rga13.12.png\|center\|600px]]

	</li>		</li>
	<li>The QCP can be used to calculate the optimum overhaul interval, as shown next.		<li>The QCP can be used to calculate the optimum overhaul interval, as shown next.

	[[Image:rga13.13.png~~\|thumb~~\|center\|450px~~\|The optimum overhaul interval.~~]]		[[Image:rga13.13.png\|center\|450px]]

	</li>		</li>

Chris Kahn at 20:08, 6 February 2014

2014-02-06T20:08:25Z

← Older revision		Revision as of 20:08, 6 February 2014
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	Field data have been collected for a system that begins its wearout phase at time zero. The start time for each system is equal to zero and the end time for each system is 10,000 miles. Each system is scheduled to undergo an overhaul after a certain number of miles. It has been determined that the cost of an overhaul is four times more expensive than a repair. The table below presents the data. Do the following:		Field data have been collected for a system that begins its wearout phase at time zero. The start time for each system is equal to zero and the end time for each system is 10,000 miles. Each system is scheduled to undergo an overhaul after a certain number of miles. It has been determined that the cost of an overhaul is four times more expensive than a repair. The table below presents the data. Do the following:

	~~:1)~~ Estimate the parameters of the Power Law model.		#Estimate the parameters of the Power Law model.
	~~:2)~~ Determine the optimum overhaul interval.		#Determine the optimum overhaul interval.
	~~:3)~~ If <math>\beta <1\,\!</math>, would it be cost-effective to implement an overhaul policy?		#If <math>\beta <1\,\!</math>, would it be cost-effective to implement an overhaul policy?

	{\|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 next figure shows the estimated Power Law parameters.		<ol>
			<li>The next figure shows the estimated Power Law parameters.

	[[Image:rga13.12.png\|thumb\|center\|450px\|Entered data and the estimated Power Law parameters.]]		[[Image:rga13.12.png\|thumb\|center\|450px\|Entered data and the estimated Power Law parameters.]]

	~~:2)~~ The QCP can be used to calculate the optimum overhaul interval, as shown next.		</li>
			<li>The QCP can be used to calculate the optimum overhaul interval, as shown next.

	[[Image:rga13.13.png\|thumb\|center\|450px\|The optimum overhaul interval.]]		[[Image:rga13.13.png\|thumb\|center\|450px\|The optimum overhaul interval.]]

	~~:3)~~ Since <math>\beta <1\,\!</math> then the systems are not wearing out and it would not be cost-effective to implement an overhaul policy. An overhaul policy makes sense only if the systems are wearing out. Otherwise, an overhauled unit would have the same probability of failing as a unit that was not overhauled.		</li>
			<li>Since <math>\beta <1\,\!</math> then the systems are not wearing out and it would not be cost-effective to implement an overhaul policy. An overhaul policy makes sense only if the systems are wearing out. Otherwise, an overhauled unit would have the same probability of failing as a unit that was not overhauled.
			</li>
			</ol>

Kate Racaza at 18:37, 4 February 2014

2014-02-04T18:37:27Z

← Older revision		Revision as of 18:37, 4 February 2014
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	<noinclude>{{Banner RGA Examples~~}}{{Navigation box~~}}		<noinclude>{{Banner RGA Examples}}
	''~~These examples appear~~ in the [[Repairable_Systems_Analysis\|Reliability Growth and Repairable System Analysis Reference book]]''.		''This example appears in the [[Repairable_Systems_Analysis\|Reliability Growth and Repairable System Analysis Reference book]]''.
	</noinclude>		</noinclude>

Kate Racaza: Created page with '{{Banner RGA Examples}}{{Navigation box}} ''These examples appear in the [[Repairable_Systems_Analysis|Reliability Growth and Repairable System Analysis Reference book…'

2014-01-29T19:04:49Z

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

New page

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

Field data have been collected for a system that begins its wearout phase at time zero. The start time for each system is equal to zero and the end time for each system is 10,000 miles. Each system is scheduled to undergo an overhaul after a certain number of miles. It has been determined that the cost of an overhaul is four times more expensive than a repair. The table below presents the data. Do the following:

:1) Estimate the parameters of the Power Law model.
:2) Determine the optimum overhaul interval.
:3) If <math>\beta <1\,\!</math>, would it be cost-effective to implement an overhaul policy?

{|border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
|-
|colspan="3" style="text-align:center"|'''Field data'''
|-
!System 1
!System 2
!System 3
|-
|1006.3|| 722.7|| 619.1
|-
|2261.2|| 1950.9|| 1519.1
|-
|2367|| 3259.6|| 2956.6
|-
|2615.5|| 4733.9|| 3114.8
|-
|2848.1|| 5105.1|| 3657.9
|-
|4073|| 5624.1|| 4268.9
|-
|5708.1|| 5806.3|| 6690.2
|-
|6464.1|| 5855.6|| 6803.1
|-
|6519.7|| 6325.2|| 7323.9
|-
|6799.1 ||6999.4|| 7501.4
|-
|7342.9 ||7084.4|| 7641.2
|-
|7736 ||7105.9|| 7851.6
|-
|8246.1|| 7290.9|| 8147.6
|-
| || 7614.2|| 8221.9
|-
| || 8332.1|| 9560.5
|-
| || 8368.5|| 9575.4
|-
| || 8947.9||
|-
| || 9012.3 ||
|-
| || 9135.9 ||
|-
| || 9147.5 ||
|-
| || 9601 ||
|}

'''Solution'''
:1) The next figure shows the estimated Power Law parameters.

[[Image:rga13.12.png|thumb|center|450px|Entered data and the estimated Power Law parameters.]]

:2) The QCP can be used to calculate the optimum overhaul interval, as shown next.

[[Image:rga13.13.png|thumb|center|450px|The optimum overhaul interval.]]

:3) Since <math>\beta <1\,\!</math> then the systems are not wearing out and it would not be cost-effective to implement an overhaul policy. An overhaul policy makes sense only if the systems are wearing out. Otherwise, an overhauled unit would have the same probability of failing as a unit that was not overhauled.