Example: Parametric RDA - Air Condition Unit - Revision history

Lisa Hacker at 18:52, 18 September 2023

2023-09-18T18:52:32Z

← Older revision		Revision as of 18:52, 18 September 2023
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [~~[Recurrent_Event_Data_Analysis#Parametric_Recurrent_Event_Data_Analysis\|~~Life ~~Data Analysis Reference book]~~]''.		''This example appears in the [https://help.reliasoft.com/reference/life_data_analysis Life data analysis reference]''.

	</noinclude>The following table gives the failure times for the air conditioning unit of an aircraft. The observation ended by the time the last failure occurred, as discussed in Cox [[Appendix:_Life_Data_Analysis_References\|[3]]].		</noinclude>The following table gives the failure times for the air conditioning unit of an aircraft. The observation ended by the time the last failure occurred, as discussed in Cox [[Appendix:_Life_Data_Analysis_References\|[3]]].

Lisa Hacker at 21:26, 10 December 2015

2015-12-10T21:26:15Z

← Older revision		Revision as of 21:26, 10 December 2015
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	:4. Using the QCP, the failure number and instantaneous failure intensity are:		:4. Using the QCP, the failure number and instantaneous failure intensity are:

	[[Image:QCP N(T).png\|center\|~~600px~~]]		[[Image:QCP N(T).png\|center\|650px]]


	[[Image:QCP Lambda(T).png\|center\|~~600px~~]]		[[Image:QCP Lambda(T).png\|center\|650px]]

Lisa Hacker at 21:25, 10 December 2015

2015-12-10T21:25:47Z

← Older revision		Revision as of 21:25, 10 December 2015
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	:2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.		:2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.

	[[Image:Parametric RDA N(T) plot.png\|center\|~~550px~~]]		[[Image:Parametric RDA N(T) plot.png\|center\|650px]]


	[[Image:Parametric RDA Lambda(T) plot.png\|center\|~~550px~~]]		[[Image:Parametric RDA Lambda(T) plot.png\|center\|650px]]

	:3. The following plot shows the conditional reliability.		:3. The following plot shows the conditional reliability.

	[[Image:Parametric RDA Cond R(T) plot.png\|center\|~~550px~~]]		[[Image:Parametric RDA Cond R(T) plot.png\|center\|650px]]

	:4. Using the QCP, the failure number and instantaneous failure intensity are:		:4. Using the QCP, the failure number and instantaneous failure intensity are:

Richard House at 21:36, 26 September 2012

2012-09-26T21:36:51Z

← Older revision		Revision as of 21:36, 26 September 2012
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	\text{268} & \text{544} & \text{950} & \text{1362} & \text{1539} \\		\text{268} & \text{544} & \text{950} & \text{1362} & \text{1539} \\
	\text{290} & \text{732} & \text{955} & \text{1459} & {} \\		\text{290} & \text{732} & \text{955} & \text{1459} & {} \\
	\end{matrix}</math></center>		\end{matrix}\,\!</math></center>

	1. Estimate the GRP model parameters using the Type I virtual age option.		1. Estimate the GRP model parameters using the Type I virtual age option.
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	Enter the data into a parametric RDA folio in Weibull++. On the control panel, select the '''3''' parameters option and the '''Type I''' setting. Keep the default simulation settings. Click '''Calculate'''.		Enter the data into a parametric RDA folio in Weibull++. On the control panel, select the '''3''' parameters option and the '''Type I''' setting. Keep the default simulation settings. Click '''Calculate'''.

	:1. The estimated parameters are <math>\hat{\beta }=1.1976,</math> <math>\hat{\lambda }=4.94E-03,</math> <math>\hat{q}=0.1344</math> .		:1. The estimated parameters are <math>\hat{\beta }=1.1976\,\!</math>, <math>\hat{\lambda }=4.94E-03\,\!</math>, <math>\hat{q}=0.1344\,\!</math>.

	:2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.		:2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.

Richard House at 17:15, 5 September 2012

2012-09-05T17:15:49Z

← Older revision		Revision as of 17:15, 5 September 2012
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	''This example appears in the [[Recurrent_Event_Data_Analysis#Parametric_Recurrent_Event_Data_Analysis\|Life Data Analysis Reference book]]''.		''This example appears in the [[Recurrent_Event_Data_Analysis#Parametric_Recurrent_Event_Data_Analysis\|Life Data Analysis Reference book]]''.

	</noinclude>The following table gives the failure times for the air conditioning unit of an aircraft. The observation ended by the time the last failure occurred.[[Appendix: ~~Weibull References~~\|[3]]]		</noinclude>The following table gives the failure times for the air conditioning unit of an aircraft. The observation ended by the time the last failure occurred, as discussed in Cox [[Appendix:_Life_Data_Analysis_References\|[3]]].

	<center><math>\begin{matrix}		<center><math>\begin{matrix}

Richard House at 05:35, 8 August 2012

2012-08-08T05:35:09Z

← Older revision		Revision as of 05:35, 8 August 2012
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	:2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.		:2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.

	[[Image:Parametric RDA N(T) plot.png\|center\|~~500px~~]]		[[Image:Parametric RDA N(T) plot.png\|center\|550px]]


	[[Image:Parametric RDA Lambda(T) plot.png\|center\|~~500px~~]]		[[Image:Parametric RDA Lambda(T) plot.png\|center\|550px]]

	:3. The following plot shows the conditional reliability.		:3. The following plot shows the conditional reliability.

	[[Image:Parametric RDA Cond R(T) plot.png\|center\|~~500px~~]]		[[Image:Parametric RDA Cond R(T) plot.png\|center\|550px]]

	:4. Using the QCP, the failure number and instantaneous failure intensity are:		:4. Using the QCP, the failure number and instantaneous failure intensity are:

Richard House at 07:50, 7 August 2012

2012-08-07T07:50:55Z

Richard House at 07:14, 6 August 2012

2012-08-06T07:14:24Z

← Older revision		Revision as of 07:14, 6 August 2012
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	[[Image:Parametric RDA N(T) plot.png~~\|thumb~~\|center\|500px]]		[[Image:Parametric RDA N(T) plot.png\|center\|500px]]
	[[Image:Parametric RDA Lambda(T) plot.png~~\|thumb~~\|center\|500px]]

			[[Image:Parametric RDA Lambda(T) plot.png\|center\|500px]]


	:3. The following plot shows the conditional reliability.		:3. The following plot shows the conditional reliability.

	[[Image:Parametric RDA Cond R(T) plot.png~~\|thumb~~\|center\|500px]]		[[Image:Parametric RDA Cond R(T) plot.png\|center\|500px]]

	:4. Using the QCP, the failure number and instantaneous failure intensity are:		:4. Using the QCP, the failure number and instantaneous failure intensity are:

	[[Image:QCP N(T).png~~\|thumb~~\|center\|600px]]		[[Image:QCP N(T).png\|center\|600px]]


	[[Image:QCP Lambda(T).png~~\|thumb~~\|center\|600px]]		[[Image:QCP Lambda(T).png\|center\|600px]]

Richard House at 07:44, 3 August 2012

2012-08-03T07:44:12Z

← Older revision		Revision as of 07:44, 3 August 2012
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	[[Image:Parametric RDA N(T) plot.png\|thumb\|center\|~~400px~~]]		[[Image:Parametric RDA N(T) plot.png\|thumb\|center\|500px]]
	[[Image:Parametric RDA Lambda(T) plot.png\|thumb\|center\|~~400px~~]]		[[Image:Parametric RDA Lambda(T) plot.png\|thumb\|center\|500px]]


	:3. The following plot shows the conditional reliability.		:3. The following plot shows the conditional reliability.

	[[Image:Parametric RDA Cond R(T) plot.png\|thumb\|center\|~~400px~~]]		[[Image:Parametric RDA Cond R(T) plot.png\|thumb\|center\|500px]]

	:4. Using the QCP, the failure number and instantaneous failure intensity are:		:4. Using the QCP, the failure number and instantaneous failure intensity are:

	[[Image:QCP N(T).png\|thumb\|center\|~~400px~~]]		[[Image:QCP N(T).png\|thumb\|center\|600px]]

	[[Image:QCP Lambda(T).png\|thumb\|center\|~~400px~~]]		[[Image:QCP Lambda(T).png\|thumb\|center\|600px]]

Kate Racaza at 04:42, 31 July 2012

2012-07-31T04:42:30Z

← Older revision		Revision as of 04:42, 31 July 2012
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	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [[Recurrent_Event_Data_Analysis#~~Bounds_on_Conditional_Reliability~~\|Life Data Analysis Reference book]]''.		''This example appears in the [[Recurrent_Event_Data_Analysis#Parametric_Recurrent_Event_Data_Analysis\|Life Data Analysis Reference book]]''.

← Older revision		Revision as of 07:14, 6 August 2012
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	[[Image:Parametric RDA N(T) plot.png~~\|thumb~~\|center\|500px]]		[[Image:Parametric RDA N(T) plot.png\|center\|500px]]
	[[Image:Parametric RDA Lambda(T) plot.png~~\|thumb~~\|center\|500px]]

			[[Image:Parametric RDA Lambda(T) plot.png\|center\|500px]]


	:3. The following plot shows the conditional reliability.		:3. The following plot shows the conditional reliability.

	[[Image:Parametric RDA Cond R(T) plot.png~~\|thumb~~\|center\|500px]]		[[Image:Parametric RDA Cond R(T) plot.png\|center\|500px]]

	:4. Using the QCP, the failure number and instantaneous failure intensity are:		:4. Using the QCP, the failure number and instantaneous failure intensity are:

	[[Image:QCP N(T).png~~\|thumb~~\|center\|600px]]		[[Image:QCP N(T).png\|center\|600px]]


	[[Image:QCP Lambda(T).png~~\|thumb~~\|center\|600px]]		[[Image:QCP Lambda(T).png\|center\|600px]]

← Older revision		Revision as of 07:44, 3 August 2012
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	[[Image:Parametric RDA N(T) plot.png\|thumb\|center\|~~400px~~]]		[[Image:Parametric RDA N(T) plot.png\|thumb\|center\|500px]]
	[[Image:Parametric RDA Lambda(T) plot.png\|thumb\|center\|~~400px~~]]		[[Image:Parametric RDA Lambda(T) plot.png\|thumb\|center\|500px]]


	:3. The following plot shows the conditional reliability.		:3. The following plot shows the conditional reliability.

	[[Image:Parametric RDA Cond R(T) plot.png\|thumb\|center\|~~400px~~]]		[[Image:Parametric RDA Cond R(T) plot.png\|thumb\|center\|500px]]

	:4. Using the QCP, the failure number and instantaneous failure intensity are:		:4. Using the QCP, the failure number and instantaneous failure intensity are:

	[[Image:QCP N(T).png\|thumb\|center\|~~400px~~]]		[[Image:QCP N(T).png\|thumb\|center\|600px]]

	[[Image:QCP Lambda(T).png\|thumb\|center\|~~400px~~]]		[[Image:QCP Lambda(T).png\|thumb\|center\|600px]]

← Older revision		Revision as of 07:50, 7 August 2012
Line 1:		Line 1:
	<noinclude>{{Banner Weibull Examples}}		<noinclude>{{Banner Weibull Examples}}
	''This example appears in the [[Recurrent_Event_Data_Analysis#Parametric_Recurrent_Event_Data_Analysis\|Life Data Analysis Reference book]]''.		''This example appears in the [[Recurrent_Event_Data_Analysis#Parametric_Recurrent_Event_Data_Analysis\|Life Data Analysis Reference book]]''.


	</noinclude>The following table gives the failure times for the air conditioning unit of an aircraft. The observation ended by the time the last failure occurred.[[Appendix: Weibull References\|[3]]]		</noinclude>The following table gives the failure times for the air conditioning unit of an aircraft. The observation ended by the time the last failure occurred.[[Appendix: Weibull References\|[3]]]


	<center><math>\begin{matrix}		<center><math>\begin{matrix}
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	\text{290} & \text{732} & \text{955} & \text{1459} & {} \\		\text{290} & \text{732} & \text{955} & \text{1459} & {} \\
	\end{matrix}</math></center>		\end{matrix}</math></center>


	1. Estimate the GRP model parameters using the Type I virtual age option.		1. Estimate the GRP model parameters using the Type I virtual age option.
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	4. Using the QCP, calculate the expected failure number and expected instantaneous failure intensity by time 1800.		4. Using the QCP, calculate the expected failure number and expected instantaneous failure intensity by time 1800.

	~~<br>~~'''Solution'''		'''Solution'''

	Enter the data into a parametric RDA folio in Weibull++. On the control panel, select the '''3''' parameters option and the '''Type I''' setting. Keep the default simulation settings. Click '''Calculate'''.		Enter the data into a parametric RDA folio in Weibull++. On the control panel, select the '''3''' parameters option and the '''Type I''' setting. Keep the default simulation settings. Click '''Calculate'''.


	:1. The estimated parameters are <math>\hat{\beta }=1.1976,</math> <math>\hat{\lambda }=4.94E-03,</math> <math>\hat{q}=0.1344</math> .		:1. The estimated parameters are <math>\hat{\beta }=1.1976,</math> <math>\hat{\lambda }=4.94E-03,</math> <math>\hat{q}=0.1344</math> .

	:2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.		:2. The following plots show the cumulative number of failures and instantaneous failure intensity, respectively.


	[[Image:Parametric RDA N(T) plot.png\|center\|500px]]		[[Image:Parametric RDA N(T) plot.png\|center\|500px]]
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	[[Image:Parametric RDA Lambda(T) plot.png\|center\|500px]]		[[Image:Parametric RDA Lambda(T) plot.png\|center\|500px]]


	:3. The following plot shows the conditional reliability.		:3. The following plot shows the conditional reliability.