Template:Generalized eyring relationship - Revision history

Richard House: Redirected page to Eyring Relationship#Generalized Eyring Relationship

2012-08-17T00:31:51Z

Redirected page to Eyring Relationship#Generalized Eyring Relationship

← Older revision		Revision as of 00:31, 17 August 2012
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	~~=Generalized Eyring Relationship=~~		#REDIRECT [[Eyring_Relationship#Generalized_Eyring_Relationship]]

	~~==Introduction==~~

	~~<br>~~
	The generalized Eyring relationship is used when temperature and a second non-thermal stress (e.g. voltage) are the accelerated stresses of a test and their interaction is also of interest. This relationship is given by:

	~~<br>~~
	~~::<math>L(V,U)=\frac{1}{V}{{e}^{A+\tfrac{B}{V}+CU+D\tfrac{U}{V}}}</math>~~

	~~<br>~~
	~~where:~~
	~~<br>~~
	~~• is the temperature ('''in absolute units''').~~

	~~• <math>U</math> is the non-thermal stress (i.e. voltage, vibration, etc.).~~
	~~<math>A,B,C,D</math> are the parameters to be determined.~~


	~~<br>~~
	~~The Eyring relationship is a simple case of the generalized Eyring relationship where <math>C=D=0</math> and <math>{{A}_{Eyr}}=-{{A}_{GEyr}}.</math>~~
	Note that the generalized Eyring relationship includes the interaction term of <math>U</math> and <math>V</math> as described by the <math>D\tfrac{U}{V}</math> term. In other words, this model can estimate the effect of changing one of the factors depending on the level of the other factor.

	~~{{gen-eyring acceleration factor}}~~

	~~{{generalized eyring-exponential}}~~

	~~{{generalized eyring-weibull}}~~

	~~{{generalized eyring-log}}~~

	~~{{Example:GER}}~~

Chris Kahn: /* Introduction */

2012-03-09T18:02:40Z

Introduction

← Older revision		Revision as of 18:02, 9 March 2012
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	where:		where:
	<br>		<br>
	• is the temperature ('''in absolute units''' ).		• is the temperature ('''in absolute units''').

	• <math>U</math> is the non-thermal stress (i.e. voltage, vibration, etc.).		• <math>U</math> is the non-thermal stress (i.e. voltage, vibration, etc.).

Athanasios Gerokostopoulos: /* Introduction */

2012-02-27T23:56:58Z

Introduction

← Older revision		Revision as of 23:56, 27 February 2012
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	<br>		<br>
	where:		where:

	<br>		<br>
	• is the temperature ('''in absolute units''' ).		• is the temperature ('''in absolute units''' ).

Athanasios Gerokostopoulos: /* Introduction */

2012-02-27T23:55:49Z

Introduction

← Older revision		Revision as of 23:55, 27 February 2012
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	<br>		<br>
	:where:		where:

	<br>		<br>

Athanasios Gerokostopoulos: /* Introduction */

2012-02-15T01:20:49Z

Introduction

← Older revision		Revision as of 01:20, 15 February 2012
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	=Generalized Eyring Relationship=		=Generalized Eyring Relationship=

	===Introduction===		==Introduction==

	<br>		<br>

Athanasios Gerokostopoulos: /* Generalized Eyring Relationship */

2012-02-15T01:20:35Z

Generalized Eyring Relationship

← Older revision		Revision as of 01:20, 15 February 2012
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	==Generalized Eyring Relationship==		=Generalized Eyring Relationship=

	===Introduction===		===Introduction===

Athanasios Gerokostopoulos: /* Introduction */

2012-02-14T23:59:26Z

Introduction

← Older revision		Revision as of 23:59, 14 February 2012
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	<br>		<br>
	• is the temperature (in absolute units ).		• is the temperature ('''in absolute units''' ).

	• <math>U</math> is the non-thermal stress (i.e. voltage, vibration, etc.).		• <math>U</math> is the non-thermal stress (i.e. voltage, vibration, etc.).

Nicolette Young: /* Example */

2012-02-14T17:54:28Z

Example

← Older revision		Revision as of 17:54, 14 February 2012
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	{{generalized eyring-log}}		{{generalized eyring-log}}

	~~===~~Example~~===~~		{{Example:GER}}
	~~<br>~~
	The following data set represents failure times (in hours) obtained from an electronics epoxy packaging accelerated life test performed to understand the synergy between temperature and humidity and estimate the <math>B10</math> life at the use conditions of <math>T=350K</math> and <math>H=0.3</math> . The data set is modeled using the lognormal distribution and the generalized Eyring model.
	~~<br>~~

	~~[[Image~~:~~altaproject.png\|thumb\|center\|400px\| ]]~~

	~~[[Image:altaaccelerated.png\|thumb\|center\|400px\| ]]~~

	~~[[Image:altatimes2fail.png\|thumb\|center\|400px\|]]~~

	~~[[Image:tempNhumin.png\|thumb\|center\|400px\|]]~~

	~~[[Image:406-1-2.png\|thumb\|center\|400px\|]]~~
	~~<math></math>~~

	~~The probability plot at the use conditions is shown next.~~

	~~<br>~~
	~~[[Image:plotfolio426.png\|thumb\|center\|400px\|]]~~
	~~<br>~~

	~~The <math>B10</math> information is estimated to be 3004.63 hours, as shown next.~~
	~~<br>~~
	~~[[Image:tempBX.png\|thumb\|center\|400px\|]]~~

	~~<br>~~

Nicolette Young: Created page with '==Generalized Eyring Relationship== ===Introduction===
The generalized Eyring relationship is used when temperature and a second non-thermal stress (e.g. voltage) are the …'

2012-01-18T16:49:33Z

Created page with '==Generalized Eyring Relationship== ===Introduction=== The generalized Eyring relationship is used when temperature and a second non-thermal stress (e.g. voltage) are the …'

New page

==Generalized Eyring Relationship==

===Introduction===

 
The generalized Eyring relationship is used when temperature and a second non-thermal stress (e.g. voltage) are the accelerated stresses of a test and their interaction is also of interest. This relationship is given by:

 
::<math>L(V,U)=\frac{1}{V}{{e}^{A+\tfrac{B}{V}+CU+D\tfrac{U}{V}}}</math>

 
:where:

 
• is the temperature (in absolute units ).

• <math>U</math> is the non-thermal stress (i.e. voltage, vibration, etc.).
<math>A,B,C,D</math> are the parameters to be determined.

 
The Eyring relationship is a simple case of the generalized Eyring relationship where <math>C=D=0</math> and <math>{{A}_{Eyr}}=-{{A}_{GEyr}}.</math>
Note that the generalized Eyring relationship includes the interaction term of <math>U</math> and <math>V</math> as described by the <math>D\tfrac{U}{V}</math> term. In other words, this model can estimate the effect of changing one of the factors depending on the level of the other factor.

{{gen-eyring acceleration factor}}

{{generalized eyring-exponential}}

{{generalized eyring-weibull}}

{{generalized eyring-log}}

===Example===
 
The following data set represents failure times (in hours) obtained from an electronics epoxy packaging accelerated life test performed to understand the synergy between temperature and humidity and estimate the <math>B10</math> life at the use conditions of <math>T=350K</math> and <math>H=0.3</math> . The data set is modeled using the lognormal distribution and the generalized Eyring model.
 

[[Image:altaproject.png|thumb|center|400px| ]]

[[Image:altaaccelerated.png|thumb|center|400px| ]]

[[Image:altatimes2fail.png|thumb|center|400px|]]

[[Image:tempNhumin.png|thumb|center|400px|]]

[[Image:406-1-2.png|thumb|center|400px|]]
<math></math>

The probability plot at the use conditions is shown next.

 
[[Image:plotfolio426.png|thumb|center|400px|]]
 

The <math>B10</math> information is estimated to be 3004.63 hours, as shown next.
 
[[Image:tempBX.png|thumb|center|400px|]]

Template:Generalized eyring relationship - Revision history

Richard House: Redirected page to Eyring Relationship#Generalized Eyring Relationship

Chris Kahn: /* Introduction */

Athanasios Gerokostopoulos: /* Introduction */

Athanasios Gerokostopoulos: /* Introduction */

Athanasios Gerokostopoulos: /* Introduction */

Athanasios Gerokostopoulos: /* Generalized Eyring Relationship */

Athanasios Gerokostopoulos: /* Introduction */

Nicolette Young: /* Example */

Nicolette Young: Created page with '==Generalized Eyring Relationship== ===Introduction=== The generalized Eyring relationship is used when temperature and a second non-thermal stress (e.g. voltage) are the …'

Nicolette Young: Created page with '==Generalized Eyring Relationship== ===Introduction===
The generalized Eyring relationship is used when temperature and a second non-thermal stress (e.g. voltage) are the …'