Reliability Importance Example - Revision history

Lisa Hacker at 20:59, 18 September 2023

2023-09-18T20:59:48Z

← Older revision		Revision as of 20:59, 18 September 2023
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	<noinclude>{{Banner BlockSim Examples}}		<noinclude>{{Banner BlockSim Examples}}
	''This example appears in the ~~article~~ [~~[Reliability Importance]~~]''.		''This example appears in the [https://help.reliasoft.com/reference/system_analysis System analysis reference]''.

	</noinclude>		</noinclude>

Richard House at 16:24, 6 January 2016

2016-01-06T16:24:15Z

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	[[Image:BS6.6.png\|center\|~~500px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>\|link=]]		[[Image:BS6.6.png\|center\|600px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>\|link=]]


	[[Image:6_7.png\|center\|~~500px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>\|link=]]		[[Image:6_7.png\|center\|600px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>\|link=]]


	[[Image:6.8.png\|center\|~~700px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>\|link=]]		[[Image:6.8.png\|center\|650px\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>\|link=]]

Richard House at 16:23, 6 January 2016

2016-01-06T16:23:19Z

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	The RBD for this example is shown next:		The RBD for this example is shown next:

	[[Image:BS6ex1.png\|center\|~~400px~~\|]]		[[Image:BS6ex1.png\|center\|500px\|]]

Richard House at 22:19, 4 January 2016

2016-01-04T22:19:20Z

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	[[Image:6.8.png\|center\|~~777px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>\|link=]]		[[Image:6.8.png\|center\|700px\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>\|link=]]

Richard House at 22:17, 4 January 2016

2016-01-04T22:17:35Z

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	[[Image:BS6.6.png\|center\|~~400px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>]]		[[Image:BS6.6.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>\|link=]]


	[[Image:6_7.png\|center\|~~400px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>]]		[[Image:6_7.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>\|link=]]


	[[Image:6.8.png\|center\|~~400px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>]]		[[Image:6.8.png\|center\|777px\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>\|link=]]

Nicolette Young at 16:40, 6 November 2012

2012-11-06T16:40:46Z

← Older revision		Revision as of 16:40, 6 November 2012
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	The RBD for this example is shown next:		The RBD for this example is shown next:

	[[Image:BS6ex1.png\|center\|~~500px~~\|]]		[[Image:BS6ex1.png\|center\|400px\|]]


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	[[Image:BS6.6.png\|center\|~~500px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>]]		[[Image:BS6.6.png\|center\|400px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>]]


	[[Image:6_7.png\|center\|~~500px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>]]		[[Image:6_7.png\|center\|400px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>]]


	[[Image:6.8.png\|center\|~~500px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>]]		[[Image:6.8.png\|center\|400px\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>]]

Richard House at 15:33, 21 September 2012

2012-09-21T15:33:39Z

Kate Racaza at 23:55, 20 August 2012

2012-08-20T23:55:35Z

← Older revision		Revision as of 23:55, 20 August 2012
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	</noinclude>		</noinclude>
	'''~~Example:~~ Reliability Importance Measures for Failure Modes'''		'''Reliability Importance Measures for Failure Modes'''

	Assume that a system has failure modes <math>A</math> , <math>B</math> , <math>C</math> , <math>D</math> , <math>E</math> and <math>F</math>. Furthermore, assume that failure of the entire system will occur if:		Assume that a system has failure modes <math>A</math> , <math>B</math> , <math>C</math> , <math>D</math> , <math>E</math> and <math>F</math>. Furthermore, assume that failure of the entire system will occur if:

Kate Racaza: Created page with '{{Banner BlockSim Examples}} ''This example appears in the article Reliability Importance''. '''Example: Reliability Importance Measures for Failure …'

2012-08-20T23:53:55Z

Created page with '<noinclude>{{Banner BlockSim Examples}} ''This example appears in the article Reliability Importance''. </noinclude> '''Example: Reliability Importance Measures for Failure …'

New page

<noinclude>{{Banner BlockSim Examples}}
''This example appears in the article [[Reliability Importance]]''.

</noinclude>
'''Example: Reliability Importance Measures for Failure Modes'''

Assume that a system has failure modes <math>A</math> , <math>B</math> , <math>C</math> , <math>D</math> , <math>E</math> and <math>F</math>. Furthermore, assume that failure of the entire system will occur if:

:• Mode <math>B</math> , <math>C</math> or <math>F</math> occurs. 
:• Modes <math>A</math> and <math>E</math> , <math>A</math> and <math>D</math> or <math>E</math> and <math>D</math> occur. 
In addition, assume the following failure probabilities for each mode.
:• Modes <math>A</math> and <math>D</math> have a mean time to occurrence of 1,000 hours (i.e., exponential with <math>MTTF=1,000).</math> 
:• Mode <math>E</math> has a mean time to occurrence of 100 hours (i.e., exponential with <math>MTTF=100).</math> 
:• Modes <math>B</math> , <math>C</math> and <math>F</math> have a mean time to occurrence of 700,000, 1,000,000 and 2,000,000 hours respectively (i.e., exponential with <math>MTT{{F}_{B}}=700,000</math>, <math>MTT{{F}_{C}}=1,000,000</math> and <math>MTT{{F}_{F}}=2,000,000).</math> 

Examine the mode importance for operating times of 100 and 500 hours.

'''Solution'''

The RBD for this example is shown next:

[[Image:BS6ex1.png|center|500px|]]

The first chart below illustrates <math>{{I}_{{{R}_{i}}}}(t=100)</math>. It can be seen that even though <math>B</math> , <math>C</math> and <math>F</math> have a much rarer rate of occurrence, they are much more significant at 100 hours. By 500 hours, <math>{{I}_{{{R}_{i}}}}(t=500)</math> , the effects of the lower reliability components become greatly pronounced and thus they become more important, as can be seen in the second chart. Finally, the behavior of <math>{{I}_{{{R}_{i}}}}(t)</math> can be observed in the Reliability Importance vs. Time plot. Note that not all lines are plainly visible in the plot due to overlap.

[[Image:BS6.6.png|center|500px|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)</math>]]

[[Image:6_7.png|center|500px|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)</math>]]

[[Image:6.8.png|center|500px|Plot of <math>{{I}_{{{R}_{i}}}}(t)</math>]]

← Older revision		Revision as of 16:24, 6 January 2016
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	[[Image:BS6.6.png\|center\|~~500px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>\|link=]]		[[Image:BS6.6.png\|center\|600px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>\|link=]]


	[[Image:6_7.png\|center\|~~500px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>\|link=]]		[[Image:6_7.png\|center\|600px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>\|link=]]


	[[Image:6.8.png\|center\|~~700px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>\|link=]]		[[Image:6.8.png\|center\|650px\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>\|link=]]

← Older revision		Revision as of 22:17, 4 January 2016
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	[[Image:BS6.6.png\|center\|~~400px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>]]		[[Image:BS6.6.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>\|link=]]


	[[Image:6_7.png\|center\|~~400px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>]]		[[Image:6_7.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>\|link=]]


	[[Image:6.8.png\|center\|~~400px~~\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>]]		[[Image:6.8.png\|center\|777px\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>\|link=]]

← Older revision		Revision as of 15:33, 21 September 2012
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	'''Reliability Importance Measures for Failure Modes'''		'''Reliability Importance Measures for Failure Modes'''

	Assume that a system has failure modes <math>A</math> , <math>B</math> , <math>C</math> , <math>D</math> , <math>E</math> and <math>F</math>. Furthermore, assume that failure of the entire system will occur if:		Assume that a system has failure modes <math>A\,\!</math>, <math>B\,\!</math>, <math>C\,\!</math>, <math>D\,\!</math>, <math>E\,\!</math> and <math>F\,\!</math>. Furthermore, assume that failure of the entire system will occur if:

	:• Mode <math>B</math> , <math>C</math> or <math>F</math> occurs.<br>		:* Mode <math>B\,\!</math>, <math>C\,\!</math> or <math>F\,\!</math> occurs.<br>
	:• Modes <math>A</math> and <math>E</math> , <math>A</math> and <math>D</math> or <math>E</math> and <math>D</math> occur.<br>		:* Modes <math>A\,\!</math> and <math>E\,\!</math>, <math>A\,\!</math> and <math>D\,\!</math> or <math>E\,\!</math> and <math>D\,\!</math> occur.<br>
	In addition, assume the following failure probabilities for each mode.		In addition, assume the following failure probabilities for each mode.
	:• Modes <math>A</math> and <math>D</math> have a mean time to occurrence of 1,000 hours (i.e., exponential with <math>MTTF=1,000).</math> <br>		:* Modes <math>A\,\!</math> and <math>D\,\!</math> have a mean time to occurrence of 1,000 hours (i.e., exponential with <math>MTTF=1,000).\,\!</math> <br>
	:• Mode <math>E</math> has a mean time to occurrence of 100 hours (i.e., exponential with <math>MTTF=100).</math> <br>		:* Mode <math>E\,\!</math> has a mean time to occurrence of 100 hours (i.e., exponential with <math>MTTF=100).\,\!</math> <br>
	:• Modes <math>B</math> , <math>C</math> and <math>F</math> have a mean time to occurrence of 700,000, 1,000,000 and 2,000,000 hours respectively (i.e., exponential with <math>MTT{{F}_{B}}=700,000</math>, <math>MTT{{F}_{C}}=1,000,000</math> and <math>MTT{{F}_{F}}=2,000,000).</math> <br>		:* Modes <math>B\,\!</math>, <math>C\,\!</math> and <math>F\,\!</math> have a mean time to occurrence of 700,000, 1,000,000 and 2,000,000 hours respectively (i.e., exponential with <math>MTT{{F}_{B}}=700,000\,\!</math>, <math>MTT{{F}_{C}}=1,000,000\,\!</math> and <math>MTT{{F}_{F}}=2,000,000).\,\!</math> <br>

	Examine the mode importance for operating times of 100 and 500 hours.		Examine the mode importance for operating times of 100 and 500 hours.
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	The first chart below illustrates <math>{{I}_{{{R}_{i}}}}(t=100)</math>. It can be seen that even though <math>B</math> , <math>C</math> and <math>F</math> have a much rarer rate of occurrence, they are much more significant at 100 hours. By 500 hours, <math>{{I}_{{{R}_{i}}}}(t=500)</math> , the effects of the lower reliability components become greatly pronounced and thus they become more important, as can be seen in the second chart. Finally, the behavior of <math>{{I}_{{{R}_{i}}}}(t)</math> can be observed in the Reliability Importance vs. Time plot. Note that not all lines are plainly visible in the plot due to overlap.		The first chart below illustrates <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>. It can be seen that even though <math>B\,\!</math>, <math>C\,\!</math> and <math>F\,\!</math> have a much rarer rate of occurrence, they are much more significant at 100 hours. By 500 hours, <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>, the effects of the lower reliability components become greatly pronounced and thus they become more important, as can be seen in the second chart. Finally, the behavior of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math> can be observed in the Reliability Importance vs. Time plot. Note that not all lines are plainly visible in the plot due to overlap.


	[[Image:BS6.6.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)</math>]]		[[Image:BS6.6.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=100)\,\!</math>]]


	[[Image:6_7.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)</math>]]		[[Image:6_7.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t=500)\,\!</math>]]


	[[Image:6.8.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t)</math>]]		[[Image:6.8.png\|center\|500px\|Plot of <math>{{I}_{{{R}_{i}}}}(t)\,\!</math>]]