Template:Gumbel probability paper - Revision history

Richard House: Redirected page to The Gumbel/SEV Distribution

2012-08-15T03:38:58Z

Redirected page to The Gumbel/SEV Distribution

← Older revision		Revision as of 03:38, 15 August 2012
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	#REDIRECT [[The_Gumbel/SEV_Distribution~~#Probability_Paper~~]]		#REDIRECT [[The_Gumbel/SEV_Distribution]]

Richard House: Redirected page to The Gumbel/SEV Distribution#Probability Paper

2012-08-15T03:38:26Z

Redirected page to The Gumbel/SEV Distribution#Probability Paper

← Older revision		Revision as of 03:38, 15 August 2012
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	~~==Probability Paper==~~		#REDIRECT [[The_Gumbel/SEV_Distribution#Probability_Paper]]
	~~The form of the Gumbel probability paper is based on a linearization of the <math>cdf</math> . From the unreliabililty equation, we know:~~

	~~::<math>z=\ln (-\ln (1-F))</math>~~

	~~using the equation for ''z'', we get:~~

	~~::<math>\frac{t-\mu }{\sigma }=\ln (-\ln (1-F))</math>~~

	~~Then:~~

	~~::<math>\ln (-\ln (1-F))=-\frac{\mu }{\sigma }+\frac{1}{\sigma }t</math>~~

	~~Now let:~~

	~~::<math>y=\ln (-\ln (1-F))</math>~~

	~~::<math>x=t</math>~~

	~~and:~~

	~~::<math>\begin{align}~~
	~~& a= & -\frac{\mu }{\sigma } \\~~
	~~& b= & \frac{1}{\sigma }~~
	~~\end{align}</math>~~


	~~which results in the linear equation of:~~

	~~::<math>y=a+bx</math>~~

	~~The Gumbel probability paper resulting from this linearized <math>cdf</math> function is shown next.~~

	[[~~Image:WB.16 probability gumbel.png\|center\|250px\|~~ ]]

	For <math>z=0</math> , <math>t=\mu </math> and <math>R(t)={{e}^{-{{e}^{0}}}}\approx 0.3678</math> (63.21% unreliability). For <math>z=1</math> , <math>\sigma =T-\mu </math> and <math>R(t)={{e}^{-{{e}^{1}}}}\approx 0.0659.</math> To read <math>\mu </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 63.21% unreliability line. To read <math>\sigma </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 93.40% unreliability line, then take the difference between this time value and the <math>\mu </math> value.

Nicolette Young: /* Probability Paper */

2012-04-25T21:59:43Z

Probability Paper

← Older revision		Revision as of 21:59, 25 April 2012
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	The Gumbel probability paper resulting from this linearized <math>cdf</math> function is shown next.		The Gumbel probability paper resulting from this linearized <math>cdf</math> function is shown next.

	[[Image:WB.16 probability gumbel.png\|center\|~~400px~~\| ]]		[[Image:WB.16 probability gumbel.png\|center\|250px\| ]]

	For <math>z=0</math> , <math>t=\mu </math> and <math>R(t)={{e}^{-{{e}^{0}}}}\approx 0.3678</math> (63.21% unreliability). For <math>z=1</math> , <math>\sigma =T-\mu </math> and <math>R(t)={{e}^{-{{e}^{1}}}}\approx 0.0659.</math> To read <math>\mu </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 63.21% unreliability line. To read <math>\sigma </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 93.40% unreliability line, then take the difference between this time value and the <math>\mu </math> value.		For <math>z=0</math> , <math>t=\mu </math> and <math>R(t)={{e}^{-{{e}^{0}}}}\approx 0.3678</math> (63.21% unreliability). For <math>z=1</math> , <math>\sigma =T-\mu </math> and <math>R(t)={{e}^{-{{e}^{1}}}}\approx 0.0659.</math> To read <math>\mu </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 63.21% unreliability line. To read <math>\sigma </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 93.40% unreliability line, then take the difference between this time value and the <math>\mu </math> value.

Nicolette Young: /* Probability Paper */

2012-03-15T17:18:47Z

Probability Paper

← Older revision		Revision as of 17:18, 15 March 2012
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	The Gumbel probability paper resulting from this linearized <math>cdf</math> function is shown next.		The Gumbel probability paper resulting from this linearized <math>cdf</math> function is shown next.

	[[Image:~~probabilitygumbel~~.~~gif\|thumb~~\|center\|400px\| ]]		[[Image:WB.16 probability gumbel.png\|center\|400px\| ]]

	For <math>z=0</math> , <math>t=\mu </math> and <math>R(t)={{e}^{-{{e}^{0}}}}\approx 0.3678</math> (63.21% unreliability). For <math>z=1</math> , <math>\sigma =T-\mu </math> and <math>R(t)={{e}^{-{{e}^{1}}}}\approx 0.0659.</math> To read <math>\mu </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 63.21% unreliability line. To read <math>\sigma </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 93.40% unreliability line, then take the difference between this time value and the <math>\mu </math> value.		For <math>z=0</math> , <math>t=\mu </math> and <math>R(t)={{e}^{-{{e}^{0}}}}\approx 0.3678</math> (63.21% unreliability). For <math>z=1</math> , <math>\sigma =T-\mu </math> and <math>R(t)={{e}^{-{{e}^{1}}}}\approx 0.0659.</math> To read <math>\mu </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 63.21% unreliability line. To read <math>\sigma </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 93.40% unreliability line, then take the difference between this time value and the <math>\mu </math> value.

Harry Guo: /* Probability Paper */

2012-02-20T18:36:31Z

Probability Paper

← Older revision		Revision as of 18:36, 20 February 2012
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	==Probability Paper==		==Probability Paper==
	The form of the Gumbel probability paper is based on a linearization of the <math>cdf</math> . From ~~Eqn. (UnrGumbel)~~:		The form of the Gumbel probability paper is based on a linearization of the <math>cdf</math> . From the unreliabililty equation, we know:

	::<math>z=\ln (-\ln (1-F))</math>		::<math>z=\ln (-\ln (1-F))</math>

			using the equation for ''z'', we get:

	:~~using Eqns.~~ (z3):		::<math>\frac{t-\mu }{\sigma }=\ln (-\ln (1-F))</math>

	:~~:<math>\frac{T-\mu }{\sigma }=\ln (-\ln (1-F))</math>~~		Then:

			::<math>\ln (-\ln (1-F))=-\frac{\mu }{\sigma }+\frac{1}{\sigma }t</math>

	~~:Then:~~		Now let:

	~~::<math>\ln (-\ln (1-F))=-\frac{\mu }{\sigma }+\frac{1}{\sigma }T</math>~~


	:Now let:

	::<math>y=\ln (-\ln (1-F))</math>		::<math>y=\ln (-\ln (1-F))</math>

			::<math>x=t</math>

	::<math>x=T</math>

			and:
	:and:

	::<math>\begin{align}		::<math>\begin{align}
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	::<math>y=a+bx</math>		::<math>y=a+bx</math>


	The Gumbel probability paper resulting from this linearized <math>cdf</math> function is shown next.		The Gumbel probability paper resulting from this linearized <math>cdf</math> function is shown next.
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	[[Image:probabilitygumbel.gif\|thumb\|center\|400px\| ]]		[[Image:probabilitygumbel.gif\|thumb\|center\|400px\| ]]

	For <math>z=0</math> , <math>T=\mu </math> and <math>R(t)={{e}^{-{{e}^{0}}}}\approx 0.3678</math> (63.21% unreliability). For <math>z=1</math> , <math>\sigma =T-\mu </math> and <math>R(t)={{e}^{-{{e}^{1}}}}\approx 0.0659.</math> To read <math>\mu </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 63.21% unreliability line. To read <math>\sigma </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 93.40% unreliability line, then take the difference between this time value and the <math>\mu </math> value.		For <math>z=0</math> , <math>t=\mu </math> and <math>R(t)={{e}^{-{{e}^{0}}}}\approx 0.3678</math> (63.21% unreliability). For <math>z=1</math> , <math>\sigma =T-\mu </math> and <math>R(t)={{e}^{-{{e}^{1}}}}\approx 0.0659.</math> To read <math>\mu </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 63.21% unreliability line. To read <math>\sigma </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 93.40% unreliability line, then take the difference between this time value and the <math>\mu </math> value.

Harry Guo at 18:22, 20 February 2012

2012-02-20T18:22:16Z

← Older revision		Revision as of 18:22, 20 February 2012
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	===Probability Paper===		==Probability Paper==
	The form of the Gumbel probability paper is based on a linearization of the <math>cdf</math> . From Eqn. (UnrGumbel):		The form of the Gumbel probability paper is based on a linearization of the <math>cdf</math> . From Eqn. (UnrGumbel):

Nicolette Young: Created page with '===Probability Paper=== The form of the Gumbel probability paper is based on a linearization of the $cdf$ . From Eqn. (UnrGumbel): :: $z=\ln (-\ln (1-F))$ …'

2012-01-04T22:51:01Z

Created page with '===Probability Paper=== The form of the Gumbel probability paper is based on a linearization of the <math>cdf</math> . From Eqn. (UnrGumbel): ::<math>z=\ln (-\ln (1-F))</math>…'

New page

===Probability Paper===
The form of the Gumbel probability paper is based on a linearization of the <math>cdf</math> . From Eqn. (UnrGumbel):

::<math>z=\ln (-\ln (1-F))</math>

:using Eqns. (z3):

::<math>\frac{T-\mu }{\sigma }=\ln (-\ln (1-F))</math>

:Then:

::<math>\ln (-\ln (1-F))=-\frac{\mu }{\sigma }+\frac{1}{\sigma }T</math>

:Now let:

::<math>y=\ln (-\ln (1-F))</math>

::<math>x=T</math>

:and:

::<math>\begin{align}
& a= & -\frac{\mu }{\sigma } \\
& b= & \frac{1}{\sigma }
\end{align}</math>

which results in the linear equation of:

::<math>y=a+bx</math>

The Gumbel probability paper resulting from this linearized <math>cdf</math> function is shown next.

[[Image:probabilitygumbel.gif|thumb|center|400px| ]]

For <math>z=0</math> , <math>T=\mu </math> and <math>R(t)={{e}^{-{{e}^{0}}}}\approx 0.3678</math> (63.21% unreliability). For <math>z=1</math> , <math>\sigma =T-\mu </math> and <math>R(t)={{e}^{-{{e}^{1}}}}\approx 0.0659.</math> To read <math>\mu </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 63.21% unreliability line. To read <math>\sigma </math> from the plot, find the time value that corresponds to the intersection of the probability plot with the 93.40% unreliability line, then take the difference between this time value and the <math>\mu </math> value.

Template:Gumbel probability paper - Revision history

Richard House: Redirected page to The Gumbel/SEV Distribution

Richard House: Redirected page to The Gumbel/SEV Distribution#Probability Paper

Nicolette Young: /* Probability Paper */

Nicolette Young: /* Probability Paper */

Harry Guo: /* Probability Paper */

Harry Guo at 18:22, 20 February 2012

Nicolette Young: Created page with '===Probability Paper=== The form of the Gumbel probability paper is based on a linearization of the cdf . From Eqn. (UnrGumbel): ::z=\ln (-\ln (1-F))…'

Nicolette Young: Created page with '===Probability Paper=== The form of the Gumbel probability paper is based on a linearization of the $cdf$ . From Eqn. (UnrGumbel): :: $z=\ln (-\ln (1-F))$ …'