Parametric Recurrent Events Data Analysis - Revision history

Kate Racaza: Redirected page to Recurrent Event Data Analysis

2012-06-28T14:39:55Z

Redirected page to Recurrent Event Data Analysis

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	~~{{Weibull Parametric~~ Recurrent ~~Events~~ Data Analysis}}		#REDIRECT [[Recurrent Event Data Analysis]]

Harry Guo at 00:41, 14 February 2012

2012-02-14T00:41:20Z

← Older revision		Revision as of 00:41, 14 February 2012
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	{{Parametric Recurrent Events Data Analysis}}		{{Weibull Parametric Recurrent Events Data Analysis}}

Harry Guo at 00:28, 14 February 2012

2012-02-14T00:28:06Z

← Older revision		Revision as of 00:28, 14 February 2012
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	{{~~parametric recurrence data analysis~~}}		{{Parametric Recurrent Events Data Analysis}}

Harry Guo: moved Template:Parametric Recurrent Events Data Analysis to Parametric Recurrent Events Data Analysis over redirect

2012-02-14T00:26:53Z

moved Template:Parametric Recurrent Events Data Analysis to Parametric Recurrent Events Data Analysis over redirect

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Harry Guo at 00:23, 14 February 2012

2012-02-14T00:23:15Z

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	~~{{template:LDABOOK\|18\|Parametric Recurrence Data Analysis}}~~


	{{parametric recurrence data analysis}}		{{parametric recurrence data analysis}}

Harry Guo: moved Parametric Recurrent Events Data Analysis to Template:Parametric Recurrent Events Data Analysis

2012-02-14T00:15:35Z

moved Parametric Recurrent Events Data Analysis to Template:Parametric Recurrent Events Data Analysis

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Nicolette Young: /* Parametric Recurrence Data Analysis */

2012-01-04T23:28:53Z

Parametric Recurrence Data Analysis

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Nicolette Young: /* Solution to Example 4 */

2011-10-05T21:15:34Z

Solution to Example 4

← Older revision		Revision as of 21:15, 5 October 2011
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	:4. Using QCP, the failure number and instantaneous failure intensity are:		:4. Using QCP, the failure number and instantaneous failure intensity are:

	~~[[Image:lda18.4.gif\|thumb\|center\|300px\| ]]~~

	~~[[Image:lda18.5.gif\|thumb\|center\|300px\| ]]~~
	<br>		<br>

Nicolette Young at 21:39, 19 August 2011

2011-08-19T21:39:13Z

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Nicolette Young: /* Bounds of Cumulative Failure (Event) Numbers */

2011-08-19T21:36:40Z

Bounds of Cumulative Failure (Event) Numbers

← Older revision		Revision as of 21:36, 19 August 2011
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	In general, in order to obtain the virtual age, the exact occurrence time of each event (failure) should be available, see Eqns.(Type I) and (Type 2). However, the times are unknown until the corresponding events occur. For this reason, there are no closed-form expressions for total failure number and failure intensity, which are functions of failure times and virtual age. Therefore, in Weibull++, Monte Carlo simulation is used to predict values of virtual time, failure number, MTBF and failure rate. The approximate confidence bounds obtained from simulation are provided. The uncertainty of model parameters is also considered in the bounds.		In general, in order to obtain the virtual age, the exact occurrence time of each event (failure) should be available, see Eqns.(Type I) and (Type 2). However, the times are unknown until the corresponding events occur. For this reason, there are no closed-form expressions for total failure number and failure intensity, which are functions of failure times and virtual age. Therefore, in Weibull++, Monte Carlo simulation is used to predict values of virtual time, failure number, MTBF and failure rate. The approximate confidence bounds obtained from simulation are provided. The uncertainty of model parameters is also considered in the bounds.
	====Bounds of Cumulative Failure (Event) Numbers====		====Bounds of Cumulative Failure (Event) Numbers====

	The variance of the cumulative failure number <math>N(t)</math> is:		The variance of the cumulative failure number <math>N(t)</math> is:


	::<math>Var[N(t)]=Var\left[ E(N(t)\|\lambda ,\beta ,q) \right]+E\left[ Var(N(t)\|\lambda ,\beta ,q) \right]</math>		::<math>Var[N(t)]=Var\left[ E(N(t)\|\lambda ,\beta ,q) \right]+E\left[ Var(N(t)\|\lambda ,\beta ,q) \right]</math>
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	where <math>{{v}_{t}}</math> is the expected virtual age at time <math>t</math> and <math>Var[\lambda v_{t}^{\beta }]</math> is::		where <math>{{v}_{t}}</math> is the expected virtual age at time <math>t</math> and <math>Var[\lambda v_{t}^{\beta }]</math> is::


	::<math>\begin{align}		::<math>\begin{align}
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	& {{{\hat{m}}}_{c}}{{(t)}_{L}}= & \frac{t}{\hat{N}{{(t)}_{U}}};\text{ }{{{\hat{m}}}_{c}}{{(t)}_{U}}=\frac{t}{\hat{N}{{(t)}_{L}}}		& {{{\hat{m}}}_{c}}{{(t)}_{L}}= & \frac{t}{\hat{N}{{(t)}_{U}}};\text{ }{{{\hat{m}}}_{c}}{{(t)}_{U}}=\frac{t}{\hat{N}{{(t)}_{L}}}
	\end{align}</math>		\end{align}</math>


	====Bounds of Instantaneous Failure Intensity and MTBF====		====Bounds of Instantaneous Failure Intensity and MTBF====