Eyring Example - Revision history

Lisa Hacker at 19:02, 18 September 2023

2023-09-18T19:02:41Z

← Older revision		Revision as of 19:02, 18 September 2023
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	<noinclude>{{Banner_ALTA_Examples}}		<noinclude>{{Banner_ALTA_Examples}}
	''This example appears in the [~~[Eyring_Relationship#Eyring-Weibull\|~~Accelerated ~~Life Testing Data Analysis Reference~~]~~] book~~.''		''This example appears in the [https://help.reliasoft.com/reference/accelerated_life_testing_data_analysis Accelerated life testing reference].''

Richard House at 22:13, 21 September 2012

2012-09-21T22:13:45Z

← Older revision		Revision as of 22:13, 21 September 2012
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	The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull model, yielding:		The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull model, yielding:

			::<math>\widehat{\beta }=4.29186497\,\!</math>

	::<math>\widehat{~~\beta~~ }=4.~~29186497~~</math>		::<math>\widehat{A}=-11.08784624\,\!</math>

	~~::<math>\widehat{A}=-11.08784624</math>~~		::<math>\widehat{B}=1454.08635742\,\!</math>

	::<math>\widehat{B}=1454.08635742</math>


	Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K by using:		Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K by using:

			::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)\,\!</math>
	::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math>

	or:		or:
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	::<math>\begin{align}		::<math>\begin{align}
	& \overline{T}= & \frac{1}{323}{{e}^{-\left( -11.08784624-\tfrac{1454.08635742}{323} \right)}}\cdot \Gamma \left( \frac{1}{4.29186497}+1 \right) =16,610\text{ }hr		& \overline{T}= & \frac{1}{323}{{e}^{-\left( -11.08784624-\tfrac{1454.08635742}{323} \right)}}\cdot \Gamma \left( \frac{1}{4.29186497}+1 \right) =16,610\text{ }hr
	\end{align}</math>		\end{align}\,\!</math>

Lisa Hacker at 02:46, 16 August 2012

2012-08-16T02:46:10Z

← Older revision		Revision as of 02:46, 16 August 2012
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	[[Image:6stresstimefailed.png\|center\|350px\|''Pdf'' of the lognormal distribution with different log-std values.]]		[[Image:6stresstimefailed.png\|center\|350px\|''Pdf'' of the lognormal distribution with different log-std values.]]

	The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull ~~relationship~~ model, yielding:		The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull model, yielding:

Kate Racaza: added link to ALTA book

2012-08-14T01:30:28Z

added link to ALTA book

← Older revision		Revision as of 01:30, 14 August 2012
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	<noinclude>{{Banner_ALTA_Examples}}		<noinclude>{{Banner_ALTA_Examples}}
			''This example appears in the [[Eyring_Relationship#Eyring-Weibull\|Accelerated Life Testing Data Analysis Reference]] book.''


	</noinclude>Consider the following times-to-failure data at three different stress levels.		</noinclude>Consider the following times-to-failure data at three different stress levels.

	[[Image:6stresstimefailed.png\|center\|~~400px~~\|''Pdf'' of the lognormal distribution with different log-std values.]]		[[Image:6stresstimefailed.png\|center\|350px\|''Pdf'' of the lognormal distribution with different log-std values.]]

	The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull relationship model, yielding:		The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull relationship model, yielding:


	::<math>\widehat{\beta }=4.29186497</math>		::<math>\widehat{\beta }=4.29186497</math>
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	::<math>\widehat{B}=1454.08635742</math>		::<math>\widehat{B}=1454.08635742</math>


	Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K by using:		Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K by using:


	::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math>		::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math>

Richard House at 07:39, 7 August 2012

2012-08-07T07:39:21Z

← Older revision		Revision as of 07:39, 7 August 2012
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	<noinclude>{{Banner_ALTA_Examples}}		<noinclude>{{Banner_ALTA_Examples}}
	</noinclude>Consider the following times-to-failure data at three different stress levels.		</noinclude>Consider the following times-to-failure data at three different stress levels.
	~~<br>~~

	~~<br>~~
	~~<br>~~
	[[Image:6stresstimefailed.png\|center\|400px\|''Pdf'' of the lognormal distribution with different log-std values.]]		[[Image:6stresstimefailed.png\|center\|400px\|''Pdf'' of the lognormal distribution with different log-std values.]]
	~~<br>~~
	~~<br>~~
	The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull relationship model, yielding:		The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull relationship model, yielding:

	~~<br>~~
	::<math>\widehat{\beta }=4.29186497</math>		::<math>\widehat{\beta }=4.29186497</math>

	~~<br>~~
	::<math>\widehat{A}=-11.08784624</math>		::<math>\widehat{A}=-11.08784624</math>

	~~<br>~~
	::<math>\widehat{B}=1454.08635742</math>		::<math>\widehat{B}=1454.08635742</math>

	~~<br>~~
	Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K by using:		Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K by using:

	~~<br>~~
	::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math>		::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math>

	~~<br>~~
	or:		or:

	~~<br>~~
	::<math>\begin{align}		::<math>\begin{align}
	& \overline{T}= & \frac{1}{323}{{e}^{-\left( -11.08784624-\tfrac{1454.08635742}{323} \right)}}\cdot \Gamma \left( \frac{1}{4.29186497}+1 \right) =16,610\text{ }hr		& \overline{T}= & \frac{1}{323}{{e}^{-\left( -11.08784624-\tfrac{1454.08635742}{323} \right)}}\cdot \Gamma \left( \frac{1}{4.29186497}+1 \right) =16,610\text{ }hr
	\end{align}</math>		\end{align}</math>

	~~<br>~~

Kate Racaza: updated banner

2012-08-02T01:37:43Z

updated banner

← Older revision		Revision as of 01:37, 2 August 2012
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	{~~\| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;"~~		<noinclude>{{Banner_ALTA_Examples}}
	\|-		</noinclude>Consider the following times-to-failure data at three different stress levels.
	~~\| valign="middle" align="left" bgcolor=EEEDF7\|[[Image: ALTA-Examples-banner.png\|400px\|center]]~~
	\|}

	<br>

	Consider the following times-to-failure data at three different stress levels.
	<br>		<br>

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	<br>		<br>
	<br>		<br>
	The data set was analyzed ~~jointly and with a complete MLE solution over~~ the ~~entire data set using ReliaSoft's ALTA~~ yielding:		The data set was entered into the ALTA standard folio and analyzed using the Eyring-Weibull relationship model, yielding:

	<br>		<br>
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	<br>		<br>
	Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K using:		Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K by using:

	<br>		<br>

Chris Kahn at 15:24, 22 May 2012

2012-05-22T15:24:09Z

← Older revision		Revision as of 15:24, 22 May 2012
Line 26:		Line 26:

	<br>		<br>
	Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of ~~323K~~ using:		Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323 K using:

	<br>		<br>

Athanasios Gerokostopoulos: moved Eyring-Weibull Example to Eyring Example

2012-05-21T21:24:12Z

moved Eyring-Weibull Example to Eyring Example

← Older revision	Revision as of 21:24, 21 May 2012
(No difference)

Nikki Helms: Created page with '{| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;" |- | valign="middle" align="left" bgcolor=EEEDF7|[[Image: ALTA-Exa…'

2012-03-21T21:06:11Z

Created page with '{| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;" |- | valign="middle" align="left" bgcolor=EEEDF7|[[Image: ALTA-Exa…'

New page

{| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;"
|-
| valign="middle" align="left" bgcolor=EEEDF7|[[Image: ALTA-Examples-banner.png|400px|center]]
|}

 

Consider the following times-to-failure data at three different stress levels.
 

 
 
[[Image:6stresstimefailed.png|center|400px|''Pdf'' of the lognormal distribution with different log-std values.]]
 
 
The data set was analyzed jointly and with a complete MLE solution over the entire data set using ReliaSoft's ALTA yielding:

 
::<math>\widehat{\beta }=4.29186497</math>

 
::<math>\widehat{A}=-11.08784624</math>

 
::<math>\widehat{B}=1454.08635742</math>

 
Once the parameters of the model are defined, other life measures can be directly obtained using the appropriate equations. For example, the MTTF can be obtained for the use stress level of 323K using:

 
::<math>\overline{T}=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}}\cdot \Gamma \left( \frac{1}{\beta }+1 \right)</math>

 
or:

 
::<math>\begin{align}
& \overline{T}= & \frac{1}{323}{{e}^{-\left( -11.08784624-\tfrac{1454.08635742}{323} \right)}}\cdot \Gamma \left( \frac{1}{4.29186497}+1 \right) =16,610\text{ }hr
\end{align}</math>