Template:Ipl ex stat prop sum - Revision history

Richard House: Redirected page to Inverse Power Law (IPL) Relationship#IPL-Exponential

2012-08-15T23:02:18Z

Redirected page to Inverse Power Law (IPL) Relationship#IPL-Exponential

← Older revision		Revision as of 23:02, 15 August 2012
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	~~===~~IPL-Exponential ~~Statistical Properties Summary===~~		#REDIRECT [[Inverse_Power_Law_(IPL)_Relationship#IPL-Exponential]]
	~~<br>~~
	~~{{ipl ex mean}}~~

	~~{{ipl ex median}}~~

	~~{{ipl ex mode}}~~

	~~{{ipl ex sd}}~~

Nicolette Young: /* Standard Deviation */

2012-01-13T18:01:49Z

Standard Deviation

← Older revision		Revision as of 18:01, 13 January 2012
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	{{ipl ex mode}}		{{ipl ex mode}}

	~~====Standard Deviation====~~		{{ipl ex sd}}
	~~<br>~~
	~~The standard deviation, <math>~~{{~~\sigma }_{T}}</math> , for the IPL-exponential model is given by:~~

	~~<br>~~
	~~::<math>{{\sigma }_{T}}=\frac{1}{K{{V}^{n}~~}}~~</math>~~

	~~<br>~~

Nicolette Young: /* Mode */

2012-01-13T18:01:33Z

Mode

← Older revision		Revision as of 18:01, 13 January 2012
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	{{ipl ex median}}		{{ipl ex median}}

	~~====Mode====~~		{{ipl ex mode}}
	~~<br>~~
	~~The~~ mode~~, <math>\tilde{T~~}~~,</math> for the IPL-exponential model is given by:~~

	~~<br>~~
	~~::<math>\tilde{T~~}~~=0</math>~~

	~~<br>~~

	====Standard Deviation====		====Standard Deviation====

Nicolette Young: /* Median */

2012-01-13T18:01:04Z

Median

← Older revision		Revision as of 18:01, 13 January 2012
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	{{ipl ex mean}}		{{ipl ex mean}}

	~~====Median====~~		{{ipl ex median}}
	~~<br>~~
	~~The median, <math>\breve~~{~~T},</math> for the IPL-exponential model is given by:~~

	~~<br>~~
	~~::<math>\breve~~{~~T}=0.693\frac{1}{K{{V}^{n}~~}}~~</math>~~

	~~<br>~~

	====Mode====		====Mode====

Nicolette Young: /* Mean or MTTF */

2012-01-13T18:00:48Z

Mean or MTTF

← Older revision		Revision as of 18:00, 13 January 2012
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	===IPL-Exponential Statistical Properties Summary===		===IPL-Exponential Statistical Properties Summary===
	<br>		<br>
	~~====Mean or MTTF====~~		{{ipl ex mean}}
	~~The~~ mean~~, <math>\overline{T~~}~~,</math> or Mean Time To Failure (MTTF) for the IPL-exponential relationship is given by:~~

	~~<br>~~
	~~::<math>\begin{align}~~
	~~& \overline{T}= & \mathop{}_{0}^{\infty }t\cdot f(t,V)dt=\mathop{}_{0}^{\infty }t\cdot K{{V}^{n}}{{e}^{-K{{V}^{n}}t}}dt \\~~
	~~& = & \frac{1}{K{{V}^{n}}}~~
	~~\end{align}</math>~~

	~~<br>~~
	~~Note that the MTTF is a function of stress only and is simply equal to the IPL relationship (which is the original assumption), when using the exponential distribution.~~
	~~<br>~~
	====Median====		====Median====
	<br>		<br>

Nicolette Young: Created page with '===IPL-Exponential Statistical Properties Summary===
====Mean or MTTF==== The mean, $\overline{T},$ or Mean Time To Failure (MTTF) for the IPL-exponential relat…'

2012-01-13T17:58:38Z

Created page with '===IPL-Exponential Statistical Properties Summary=== ====Mean or MTTF==== The mean, <math>\overline{T},</math> or Mean Time To Failure (MTTF) for the IPL-exponential relat…'

New page

===IPL-Exponential Statistical Properties Summary===
 
====Mean or MTTF====
The mean, <math>\overline{T},</math> or Mean Time To Failure (MTTF) for the IPL-exponential relationship is given by:

 
::<math>\begin{align}
& \overline{T}= & \mathop{}_{0}^{\infty }t\cdot f(t,V)dt=\mathop{}_{0}^{\infty }t\cdot K{{V}^{n}}{{e}^{-K{{V}^{n}}t}}dt \\
& = & \frac{1}{K{{V}^{n}}}
\end{align}</math>

 
Note that the MTTF is a function of stress only and is simply equal to the IPL relationship (which is the original assumption), when using the exponential distribution.
 
====Median====
 
The median, <math>\breve{T},</math> for the IPL-exponential model is given by:

 
::<math>\breve{T}=0.693\frac{1}{K{{V}^{n}}}</math>

 

====Mode====
 
The mode, <math>\tilde{T},</math> for the IPL-exponential model is given by:

 
::<math>\tilde{T}=0</math>

 

====Standard Deviation====
 
The standard deviation, <math>{{\sigma }_{T}}</math> , for the IPL-exponential model is given by:

 
::<math>{{\sigma }_{T}}=\frac{1}{K{{V}^{n}}}</math>