Eyring Relationship

From ReliaWiki
Revision as of 18:14, 4 June 2012 by Lisa Hacker (talk | contribs)
Jump to navigation Jump to search

New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images, more targeted search and the latest content available as a PDF. As of September 2023, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest reference at help.reliasoft.com/reference/accelerated_life_testing_data_analysis

Chapter 5: Eyring Relationship


ALTAbox.png

Chapter 5  
Eyring Relationship  

Synthesis-icon.png

Available Software:
ALTA

Examples icon.png

More Resources:
ALTA Examples


Introduction


The Eyring relationship was formulated from quantum mechanics principles [9] and is most often used when thermal stress (temperature) is the acceleration variable. However, the Eyring relationship is also often used for stress variables other than temperature, such as humidity. The relationship is given by:


[math]\displaystyle{ L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]


where:
[math]\displaystyle{ L }[/math] represents a quantifiable life measure, such as mean life, characteristic life, median life, [math]\displaystyle{ B(x) }[/math] life, etc.

[math]\displaystyle{ V }[/math] represents the stress level (temperature values are in absolute units: kelvin or degrees Rankine).

[math]\displaystyle{ A }[/math] is one of the model parameters to be determined.

[math]\displaystyle{ B }[/math] is another model parameter to be determined.


Graphical look at the Eyring relationship (linear scale), at different life characteristics and with a Weibull life distribution.



The Eyring relationship is similar to the Arrhenius relationship. This similarity is more apparent if it is rewritten in the following way:


[math]\displaystyle{ \begin{align} L(V)=\ & \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} =\ & \frac{{{e}^{-A}}}{V}{{e}^{\tfrac{B}{V}}} \end{align} }[/math]


or:


[math]\displaystyle{ L(V)=\frac{1}{V}Const.\cdot {{e}^{\tfrac{B}{V}}} }[/math]


The Arrhenius relationship is given by:


[math]\displaystyle{ L(V)=C\cdot {{e}^{\tfrac{B}{V}}} }[/math]


Comparing the above equation to the Arrhenius relationship, it can be seen that the only difference between the two relationships is the [math]\displaystyle{ \tfrac{1}{V} }[/math] term above. In general, both relationships yield very similar results. Like the Arrhenius, the Eyring relationship is plotted on a log-reciprocal paper.

Eyring relationship plotted on Arrhenius paper.


New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images, more targeted search and the latest content available as a PDF. As of September 2023, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest reference at help.reliasoft.com/reference/accelerated_life_testing_data_analysis

Chapter 5: Eyring Relationship


ALTAbox.png

Chapter 5  
Eyring Relationship  

Synthesis-icon.png

Available Software:
ALTA

Examples icon.png

More Resources:
ALTA Examples


Introduction


The Eyring relationship was formulated from quantum mechanics principles [9] and is most often used when thermal stress (temperature) is the acceleration variable. However, the Eyring relationship is also often used for stress variables other than temperature, such as humidity. The relationship is given by:


[math]\displaystyle{ L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]


where:
[math]\displaystyle{ L }[/math] represents a quantifiable life measure, such as mean life, characteristic life, median life, [math]\displaystyle{ B(x) }[/math] life, etc.

[math]\displaystyle{ V }[/math] represents the stress level (temperature values are in absolute units: kelvin or degrees Rankine).

[math]\displaystyle{ A }[/math] is one of the model parameters to be determined.

[math]\displaystyle{ B }[/math] is another model parameter to be determined.


Graphical look at the Eyring relationship (linear scale), at different life characteristics and with a Weibull life distribution.



The Eyring relationship is similar to the Arrhenius relationship. This similarity is more apparent if it is rewritten in the following way:


[math]\displaystyle{ \begin{align} L(V)=\ & \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} =\ & \frac{{{e}^{-A}}}{V}{{e}^{\tfrac{B}{V}}} \end{align} }[/math]


or:


[math]\displaystyle{ L(V)=\frac{1}{V}Const.\cdot {{e}^{\tfrac{B}{V}}} }[/math]


The Arrhenius relationship is given by:


[math]\displaystyle{ L(V)=C\cdot {{e}^{\tfrac{B}{V}}} }[/math]


Comparing the above equation to the Arrhenius relationship, it can be seen that the only difference between the two relationships is the [math]\displaystyle{ \tfrac{1}{V} }[/math] term above. In general, both relationships yield very similar results. Like the Arrhenius, the Eyring relationship is plotted on a log-reciprocal paper.

Eyring relationship plotted on Arrhenius paper.


Template loop detected: Template:Alta e.a-e acceleration factor

Template loop detected: Template:Alta a-e.e-e

Template loop detected: Template:Alta eyring-weibull

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

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 model, yielding:

[math]\displaystyle{ \widehat{\beta }=4.29186497\,\! }[/math]
[math]\displaystyle{ \widehat{A}=-11.08784624\,\! }[/math]
[math]\displaystyle{ \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:

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

or:

[math]\displaystyle{ \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]

Template loop detected: Template:Erying-log


Template loop detected: Template:Generalized eyring


Template loop detected: Template:Eyring confidence bounds

New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images, more targeted search and the latest content available as a PDF. As of September 2023, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest reference at help.reliasoft.com/reference/accelerated_life_testing_data_analysis

Chapter 5: Eyring Relationship


ALTAbox.png

Chapter 5  
Eyring Relationship  

Synthesis-icon.png

Available Software:
ALTA

Examples icon.png

More Resources:
ALTA Examples


Introduction


The Eyring relationship was formulated from quantum mechanics principles [9] and is most often used when thermal stress (temperature) is the acceleration variable. However, the Eyring relationship is also often used for stress variables other than temperature, such as humidity. The relationship is given by:


[math]\displaystyle{ L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]


where:
[math]\displaystyle{ L }[/math] represents a quantifiable life measure, such as mean life, characteristic life, median life, [math]\displaystyle{ B(x) }[/math] life, etc.

[math]\displaystyle{ V }[/math] represents the stress level (temperature values are in absolute units: kelvin or degrees Rankine).

[math]\displaystyle{ A }[/math] is one of the model parameters to be determined.

[math]\displaystyle{ B }[/math] is another model parameter to be determined.


Graphical look at the Eyring relationship (linear scale), at different life characteristics and with a Weibull life distribution.



The Eyring relationship is similar to the Arrhenius relationship. This similarity is more apparent if it is rewritten in the following way:


[math]\displaystyle{ \begin{align} L(V)=\ & \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} =\ & \frac{{{e}^{-A}}}{V}{{e}^{\tfrac{B}{V}}} \end{align} }[/math]


or:


[math]\displaystyle{ L(V)=\frac{1}{V}Const.\cdot {{e}^{\tfrac{B}{V}}} }[/math]


The Arrhenius relationship is given by:


[math]\displaystyle{ L(V)=C\cdot {{e}^{\tfrac{B}{V}}} }[/math]


Comparing the above equation to the Arrhenius relationship, it can be seen that the only difference between the two relationships is the [math]\displaystyle{ \tfrac{1}{V} }[/math] term above. In general, both relationships yield very similar results. Like the Arrhenius, the Eyring relationship is plotted on a log-reciprocal paper.

Eyring relationship plotted on Arrhenius paper.


Template loop detected: Template:Alta e.a-e acceleration factor

Template loop detected: Template:Alta a-e.e-e

Template loop detected: Template:Alta eyring-weibull

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

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 model, yielding:

[math]\displaystyle{ \widehat{\beta }=4.29186497\,\! }[/math]
[math]\displaystyle{ \widehat{A}=-11.08784624\,\! }[/math]
[math]\displaystyle{ \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:

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

or:

[math]\displaystyle{ \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]

Template loop detected: Template:Erying-log


Template loop detected: Template:Generalized eyring


Template loop detected: Template:Eyring confidence bounds

New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images, more targeted search and the latest content available as a PDF. As of September 2023, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest reference at help.reliasoft.com/reference/accelerated_life_testing_data_analysis

Chapter 5: Eyring Relationship


ALTAbox.png

Chapter 5  
Eyring Relationship  

Synthesis-icon.png

Available Software:
ALTA

Examples icon.png

More Resources:
ALTA Examples


Introduction


The Eyring relationship was formulated from quantum mechanics principles [9] and is most often used when thermal stress (temperature) is the acceleration variable. However, the Eyring relationship is also often used for stress variables other than temperature, such as humidity. The relationship is given by:


[math]\displaystyle{ L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]


where:
[math]\displaystyle{ L }[/math] represents a quantifiable life measure, such as mean life, characteristic life, median life, [math]\displaystyle{ B(x) }[/math] life, etc.

[math]\displaystyle{ V }[/math] represents the stress level (temperature values are in absolute units: kelvin or degrees Rankine).

[math]\displaystyle{ A }[/math] is one of the model parameters to be determined.

[math]\displaystyle{ B }[/math] is another model parameter to be determined.


Graphical look at the Eyring relationship (linear scale), at different life characteristics and with a Weibull life distribution.



The Eyring relationship is similar to the Arrhenius relationship. This similarity is more apparent if it is rewritten in the following way:


[math]\displaystyle{ \begin{align} L(V)=\ & \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} =\ & \frac{{{e}^{-A}}}{V}{{e}^{\tfrac{B}{V}}} \end{align} }[/math]


or:


[math]\displaystyle{ L(V)=\frac{1}{V}Const.\cdot {{e}^{\tfrac{B}{V}}} }[/math]


The Arrhenius relationship is given by:


[math]\displaystyle{ L(V)=C\cdot {{e}^{\tfrac{B}{V}}} }[/math]


Comparing the above equation to the Arrhenius relationship, it can be seen that the only difference between the two relationships is the [math]\displaystyle{ \tfrac{1}{V} }[/math] term above. In general, both relationships yield very similar results. Like the Arrhenius, the Eyring relationship is plotted on a log-reciprocal paper.

Eyring relationship plotted on Arrhenius paper.


Template loop detected: Template:Alta e.a-e acceleration factor

Template loop detected: Template:Alta a-e.e-e

Template loop detected: Template:Alta eyring-weibull

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

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 model, yielding:

[math]\displaystyle{ \widehat{\beta }=4.29186497\,\! }[/math]
[math]\displaystyle{ \widehat{A}=-11.08784624\,\! }[/math]
[math]\displaystyle{ \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:

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

or:

[math]\displaystyle{ \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]

Template loop detected: Template:Erying-log


Template loop detected: Template:Generalized eyring


Template loop detected: Template:Eyring confidence bounds

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

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 model, yielding:

[math]\displaystyle{ \widehat{\beta }=4.29186497\,\! }[/math]
[math]\displaystyle{ \widehat{A}=-11.08784624\,\! }[/math]
[math]\displaystyle{ \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:

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

or:

[math]\displaystyle{ \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]

New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images, more targeted search and the latest content available as a PDF. As of September 2023, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest reference at help.reliasoft.com/reference/accelerated_life_testing_data_analysis

Chapter 5: Eyring Relationship


ALTAbox.png

Chapter 5  
Eyring Relationship  

Synthesis-icon.png

Available Software:
ALTA

Examples icon.png

More Resources:
ALTA Examples


Introduction


The Eyring relationship was formulated from quantum mechanics principles [9] and is most often used when thermal stress (temperature) is the acceleration variable. However, the Eyring relationship is also often used for stress variables other than temperature, such as humidity. The relationship is given by:


[math]\displaystyle{ L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]


where:
[math]\displaystyle{ L }[/math] represents a quantifiable life measure, such as mean life, characteristic life, median life, [math]\displaystyle{ B(x) }[/math] life, etc.

[math]\displaystyle{ V }[/math] represents the stress level (temperature values are in absolute units: kelvin or degrees Rankine).

[math]\displaystyle{ A }[/math] is one of the model parameters to be determined.

[math]\displaystyle{ B }[/math] is another model parameter to be determined.


Graphical look at the Eyring relationship (linear scale), at different life characteristics and with a Weibull life distribution.



The Eyring relationship is similar to the Arrhenius relationship. This similarity is more apparent if it is rewritten in the following way:


[math]\displaystyle{ \begin{align} L(V)=\ & \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} =\ & \frac{{{e}^{-A}}}{V}{{e}^{\tfrac{B}{V}}} \end{align} }[/math]


or:


[math]\displaystyle{ L(V)=\frac{1}{V}Const.\cdot {{e}^{\tfrac{B}{V}}} }[/math]


The Arrhenius relationship is given by:


[math]\displaystyle{ L(V)=C\cdot {{e}^{\tfrac{B}{V}}} }[/math]


Comparing the above equation to the Arrhenius relationship, it can be seen that the only difference between the two relationships is the [math]\displaystyle{ \tfrac{1}{V} }[/math] term above. In general, both relationships yield very similar results. Like the Arrhenius, the Eyring relationship is plotted on a log-reciprocal paper.

Eyring relationship plotted on Arrhenius paper.


Template loop detected: Template:Alta e.a-e acceleration factor

Template loop detected: Template:Alta a-e.e-e

Template loop detected: Template:Alta eyring-weibull

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

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 model, yielding:

[math]\displaystyle{ \widehat{\beta }=4.29186497\,\! }[/math]
[math]\displaystyle{ \widehat{A}=-11.08784624\,\! }[/math]
[math]\displaystyle{ \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:

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

or:

[math]\displaystyle{ \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]

Template loop detected: Template:Erying-log


Template loop detected: Template:Generalized eyring


Template loop detected: Template:Eyring confidence bounds


New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images, more targeted search and the latest content available as a PDF. As of September 2023, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest reference at help.reliasoft.com/reference/accelerated_life_testing_data_analysis

Chapter 5: Eyring Relationship


ALTAbox.png

Chapter 5  
Eyring Relationship  

Synthesis-icon.png

Available Software:
ALTA

Examples icon.png

More Resources:
ALTA Examples


Introduction


The Eyring relationship was formulated from quantum mechanics principles [9] and is most often used when thermal stress (temperature) is the acceleration variable. However, the Eyring relationship is also often used for stress variables other than temperature, such as humidity. The relationship is given by:


[math]\displaystyle{ L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]


where:
[math]\displaystyle{ L }[/math] represents a quantifiable life measure, such as mean life, characteristic life, median life, [math]\displaystyle{ B(x) }[/math] life, etc.

[math]\displaystyle{ V }[/math] represents the stress level (temperature values are in absolute units: kelvin or degrees Rankine).

[math]\displaystyle{ A }[/math] is one of the model parameters to be determined.

[math]\displaystyle{ B }[/math] is another model parameter to be determined.


Graphical look at the Eyring relationship (linear scale), at different life characteristics and with a Weibull life distribution.



The Eyring relationship is similar to the Arrhenius relationship. This similarity is more apparent if it is rewritten in the following way:


[math]\displaystyle{ \begin{align} L(V)=\ & \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} =\ & \frac{{{e}^{-A}}}{V}{{e}^{\tfrac{B}{V}}} \end{align} }[/math]


or:


[math]\displaystyle{ L(V)=\frac{1}{V}Const.\cdot {{e}^{\tfrac{B}{V}}} }[/math]


The Arrhenius relationship is given by:


[math]\displaystyle{ L(V)=C\cdot {{e}^{\tfrac{B}{V}}} }[/math]


Comparing the above equation to the Arrhenius relationship, it can be seen that the only difference between the two relationships is the [math]\displaystyle{ \tfrac{1}{V} }[/math] term above. In general, both relationships yield very similar results. Like the Arrhenius, the Eyring relationship is plotted on a log-reciprocal paper.

Eyring relationship plotted on Arrhenius paper.


Template loop detected: Template:Alta e.a-e acceleration factor

Template loop detected: Template:Alta a-e.e-e

Template loop detected: Template:Alta eyring-weibull

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

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 model, yielding:

[math]\displaystyle{ \widehat{\beta }=4.29186497\,\! }[/math]
[math]\displaystyle{ \widehat{A}=-11.08784624\,\! }[/math]
[math]\displaystyle{ \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:

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

or:

[math]\displaystyle{ \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]

Template loop detected: Template:Erying-log


Template loop detected: Template:Generalized eyring


Template loop detected: Template:Eyring confidence bounds


New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images, more targeted search and the latest content available as a PDF. As of September 2023, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest reference at help.reliasoft.com/reference/accelerated_life_testing_data_analysis

Chapter 5: Eyring Relationship


ALTAbox.png

Chapter 5  
Eyring Relationship  

Synthesis-icon.png

Available Software:
ALTA

Examples icon.png

More Resources:
ALTA Examples


Introduction


The Eyring relationship was formulated from quantum mechanics principles [9] and is most often used when thermal stress (temperature) is the acceleration variable. However, the Eyring relationship is also often used for stress variables other than temperature, such as humidity. The relationship is given by:


[math]\displaystyle{ L(V)=\frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} }[/math]


where:
[math]\displaystyle{ L }[/math] represents a quantifiable life measure, such as mean life, characteristic life, median life, [math]\displaystyle{ B(x) }[/math] life, etc.

[math]\displaystyle{ V }[/math] represents the stress level (temperature values are in absolute units: kelvin or degrees Rankine).

[math]\displaystyle{ A }[/math] is one of the model parameters to be determined.

[math]\displaystyle{ B }[/math] is another model parameter to be determined.


Graphical look at the Eyring relationship (linear scale), at different life characteristics and with a Weibull life distribution.



The Eyring relationship is similar to the Arrhenius relationship. This similarity is more apparent if it is rewritten in the following way:


[math]\displaystyle{ \begin{align} L(V)=\ & \frac{1}{V}{{e}^{-\left( A-\tfrac{B}{V} \right)}} =\ & \frac{{{e}^{-A}}}{V}{{e}^{\tfrac{B}{V}}} \end{align} }[/math]


or:


[math]\displaystyle{ L(V)=\frac{1}{V}Const.\cdot {{e}^{\tfrac{B}{V}}} }[/math]


The Arrhenius relationship is given by:


[math]\displaystyle{ L(V)=C\cdot {{e}^{\tfrac{B}{V}}} }[/math]


Comparing the above equation to the Arrhenius relationship, it can be seen that the only difference between the two relationships is the [math]\displaystyle{ \tfrac{1}{V} }[/math] term above. In general, both relationships yield very similar results. Like the Arrhenius, the Eyring relationship is plotted on a log-reciprocal paper.

Eyring relationship plotted on Arrhenius paper.


Template loop detected: Template:Alta e.a-e acceleration factor

Template loop detected: Template:Alta a-e.e-e

Template loop detected: Template:Alta eyring-weibull

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

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 model, yielding:

[math]\displaystyle{ \widehat{\beta }=4.29186497\,\! }[/math]
[math]\displaystyle{ \widehat{A}=-11.08784624\,\! }[/math]
[math]\displaystyle{ \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:

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

or:

[math]\displaystyle{ \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]

Template loop detected: Template:Erying-log


Template loop detected: Template:Generalized eyring


Template loop detected: Template:Eyring confidence bounds