Hello,
I have a question regarding the acceleration factor.
We know that the lifetime (TF) of a component can be expressed as:
(1) TF=A0exp(Ea/(kT))
where A0 is a constant (component dependent), Ea is the activation energy, k is the Boltzmann constant and T is the temperature.
For a given temperature, the larger is Ea the larger is TF.
If we test the same component at different temperature (T1 and T2), we can define an acceleration factor AF as:
(2) AF=TF1/TF2 = exp((Ea/k)*(1/T1 - 1/T2))
so we can write:
(3) TF1=TF2*AF=TF2*exp((Ea/k)*(1/T1 - 1/T2))
If T11 so if we vary Ea we find that the larger is Ea the longer is TF. This is in agreement with (1)
If T1>T2:
AF
The explanation is not difficult. You are considering AF constant with respect to Ea, while AF is not constant. If you substitute the definition of AF (eq 2) in eq. 3 you obtain again the equation 1.
Thanks Gianpiero for your answer, but I am still struggling to understand.
Let' s say that I do a test at temperature T1 and I find the value of TF1.
I want to know now the TF2 associated to T2, I apply formula (3). As I have some incertitude on the exact value of Ea I vary its value in a certain range.
- case #1: T1I find that the smaller Ea will give me a smaller TTF2
- case #2: T1>T2 -->I find that the smaller Ea will give me a larger TTF2
Is this normal or there is something wrong with this reasoning? I find case#1 in agreement with my understanding of the meaning of activation energy. On the contrary I do not understand the meaning of case#2: How is it possible that a smaller Ea gives me a longer TF?This is not in agreement with formula (1).
Thanks again
With this formula you are calculating TF2 relative to the TF1. This means that you are looking at the derivative. For T1
Just to complete, As limiting case of Ea=0 gives always TF2=TF1, i.e. the rate is independent on the temperature. To have this limit you can only the the behavior described in the question
Hi Valeria,
If I did not misunderstand that you are changing Ea and find the relation with TF and AF, even AF is constant. However, when Ea is changed, it means that you changed the mechanism of failure, which is a pitfall of the accelerated testing method.
I advise that you can read « Accelerated testing, Statistied model, test plan, and Data analysis » of W. Nelson for more detail.
Minh Tuan Truong thanks a lot for the suggested reading.
To explain you more: I am varying Ea as, depending on publication, I find different values. For this reason I want to see which value gives me the worst (so the shorter) TF. Also, all the TFs I find in publications are found at a lower temperature of the usage temperature of the component I am analysing.
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