Highly accelerated life testing using Arrhenius equation online calculator

Highly accelerated life testing is a way to save time on testing new devices. One way to conduct such tests is to use an increased test temperature. This method is most commonly used when testing electronic devices.

But how do we know how long we need to perform temperature tests to confirm an MTBF of 10,000 hours? My online calculator for highly accelerated life testing will do it quickly and easily.

For example:

ISO 26262-5 strongly recommends accelerated life testing for the ASIL-D rated hardware components during the verification stage. An electronic device under the test has the failure rate of 10E-8 1/h related to the failure mode of aging failure that violates some safety goal.

The climatic chamber that might be used for the accelerated life tests of the electronic device can support temperatures up to 200 °C , while nominal operational temperature for the electronic device is 50 °C.
Assuming datasheet says the activation energy for the failure mode of aging failure that violates the safety goal is 0.8 electron volts, please estimate how much accelerated test time will it take to define if the failure rate assigned to the failure mode is valid.

I used math model from this article.

First, we have to calculate Acceleration Factor (Af). This equation calculates the time acceleration value that results from operating a device at an elevated temperature.

here:
Ea = activation energy (eV) of the failure mode = 0,8 eV for example;
k (Boltzmann’s constant) = 8.617 x 10-5 eV/K;
T use = use temperature = 50 °C or 323 K for example;
T test = test temperature = 200 °C or 473 K for example.

Next step.

We have equation for accelerated test time:

here:

λ = failure rate = 1E-8 = 0,00000001 for example or 1/MTBF or 1/MTTF;
D = number of tested devices - we take 1;
Af = acceleration factor derived from the Arrhenius equation – we've just found it!;
X2 (Chi-squared) is the probability estimation for the number of failures or rejects;
α (alpha), confidence level (CL) or probability, is the applicable percent area under the X2 probability distribution curve; We take α = 0,9;
ν (nu), degrees of freedom (DF), determines the shape of the X2 curve; reliability calculations use ν = 2r + 2;
r = limit number of failures when we stop the test;
According to quantile table of chi distribution for α = 0,9 and ν = 6, we have X2 = 7,78.

In my first Highly accelerated life testing using Arrhenius equation online calculator I assumed that r, limit number of failures when we stop the test would be 1. That's what you do while testing unique, expensive equipment.

Please, enter numbers with a dot, not a comma. 0,992 - incorrect format. 0.992 is the correct one.

Now, let's assume that r takes on a value other than 1. Then we need again to determine ν(nu), degrees of freedom (DF), determines the shape of the X2 curve.

We have equation for this:

After we using α (alpha), confidence level (CL) or probability, is the applicable percent area under the X2 probability distribution curve and according to quantile table of chi distribution for α = 0,9 and new ν, we have new X2.

Here is another Highly accelerated life testing using Arrhenius equation online calculator for different r and X2:

Save your time, enjoy your use. Let your devices be reliable.

Alexey Glazachev, reliability engineer and teacher.