Arrhenius-Exponential Model: Difference between revisions

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{{Reference Example|ALTA_Reference_Examples_Banner.png|ALTA_Reference_Examples}}
{{Reference Example|{{Banner ALTA Reference Examples}}}}


Validate the calculation of Arrhenius-Exponential model.
This example validates the calculations for the Arrhenius-exponential model in ALTA standard folios.




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{{Reference_Example_Heading1}}


Data is from Example 7.1 on page 254 in book ''Life Cycle Reliability Engineering'' by Dr. Guangbin Yang, John Wiley & Sons, 2007.
The data set is from Example 7.1 on page 254 in book ''Life Cycle Reliability Engineering'' by Dr. Guangbin Yang, John Wiley & Sons, 2007.




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For this data set, the Arrhenius life stress relationship with an Exponential distribution is used.  The estimated activation energy value is <math>\,\!E_{a}=0.323</math>. The acceleration factor from 70°C to 35°C is 3.5.
For this data set, the Arrhenius life-stress relationship with an exponential distribution is used.  The estimated activation energy value is <math>\,\!E_{a}=0.323</math>. The acceleration factor from 70°C to 35°C is 3.5.




{{Reference_Example_Heading4|ALTA}}
{{Reference_Example_Heading4|ALTA}}


In ALTA, the temperature values are converted from degree C to degree K.
In ALTA, the temperature values given in the book are converted from Celsius to Kelvins, as shown next.


[[image:Arrhenius Exp_Folio.png|center]]
[[image:Arrhenius Exp_Folio.png|center]]

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Arrhenius-Exponential Model

This example validates the calculations for the Arrhenius-exponential model in ALTA standard folios.


Reference Case

The data set is from Example 7.1 on page 254 in book Life Cycle Reliability Engineering by Dr. Guangbin Yang, John Wiley & Sons, 2007.


Data

Failure Time Temperature (°C)
2385 85
2537 85
1655 100
1738 100
1025 115
1163 115


Result

For this data set, the Arrhenius life-stress relationship with an exponential distribution is used. The estimated activation energy value is [math]\displaystyle{ \,\!E_{a}=0.323 }[/math]. The acceleration factor from 70°C to 35°C is 3.5.


Results in ALTA

In ALTA, the temperature values given in the book are converted from Celsius to Kelvins, as shown next.

Arrhenius Exp Folio.png


The calculated activation energy is 0.323. The acceleration factor from 70°C (343.15 K) to 35°C (308.15 K) is 3.46 as shown next.

Arrhenius Exp QPC.png
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