Arrhenius-Exponential Model: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
No edit summary
No edit summary
 
(11 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Reference Example|ALTA_Reference_Examples_Banner.png|ALTA_Reference_Examples}}
{{Reference Example|{{Banner ALTA Reference Examples}}}}
 
This example validates the calculations for the Arrhenius-exponential model in ALTA standard folios.


Validate the calculation of Arrhenius-Exponential model.


{{Reference_Example_Heading1}}
{{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.




Line 27: Line 28:
|-
|-
|}
|}




{{Reference_Example_Heading3}}
{{Reference_Example_Heading3}}


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]]




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 given below.  
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.  


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

Latest revision as of 18:20, 28 September 2015

ALTA Reference Examples Banner.png


New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.

As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at ALTA examples and ALTA reference examples.



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
Retrieved from "https://www.reliawiki.com/index.php?title=Arrhenius-Exponential_Model&oldid=60832"