8.1.5.1. Arrhenius

8. Assessing Product Reliability
8.1. Introduction
8.1.5. What are some common acceleration models?

8.1.5.1. Arrhenius

The Arrhenius model predicts failure acceleration due to temperature increase

One of the earliest and most successful acceleration models predicts how time to fail varies with temperature. This empirically based model is known as the Arrhenius equation. It takes the form

where T is temperature measured in degrees Kelvin (273.16 + degrees Centigrade) at the point where the failure process takes place and k is Boltzmann's constant (8.617 x 10^-5 in eV/K). The constant A is a scaling factor that drops out when calculating acceleration factors, while

H (pronounced "Delta H") is also called the activation energy, and is the critical parameter in the model.

The Arrhenius activation energy H is all you need to know to calculate temperature acceleration

The value of

H depends on the failure mechanism and the materials involved, and typically ranges between .3 or .4 up to 1.5 or even higher. Acceleration factors between two temperatures increase exponentially as

H increases.

The acceleration factor between a higher temperature T₂ and a lower temperature T₁ is given by

Using the value of k given above, this can be written in terms of T in degrees Centigrade as

Note that the only unknown parameter in this formula is H.

Example: The acceleration factor between 25°C and 125°C is 133 if H = .5 and 17,597 if H = 1.0.

The Arrhenius model has been used successfully for failure mechanisms that depend on chemical reactions, diffusion processes or migration processes. This covers many of the non mechanical (or non material fatigue) failure modes that cause electronic equipment failure.