I have what I think is the definitive answer.
The Arrhenius equation states that failures accelerate as temperature goes up. However this equation only details failures at the *silicon* level. It does not take into account mechanical stress associated with the part heating and cooling and the device maybe expanding at a different rate to the PCB and thus, over time, causing poor solder joints etc. It also does not take into account corrosion effects that get worse as temperature goes up.
It also ignores the effect of raised temperature on the surrounding components. Leakage currents in silicon double every 10 degC rise in temperature, offset voltages get worse, analogue reference voltages drift, accuracy goes down and data memory retention deteriorates, so although you part is happy running at 125degC for the next 175,000 years (see below) the effect of temperature has a huge impact on the performance of the rest of your circuit.
Looking at
silicon only, the Arrhenius equation states that a part is 943x more likely to fail at 125degC than at 25 degC. Arrhenius is based on exp (-qV/kt) where q = 1.602 x10E-19, k = 1.38 x 10E-23, T is Kelvin and V = 0.7)
So we know the acceleration factor, but we don't know what number to start with. Looking at the failure report of a random component (LTC3891) this details a statistical failure rate of 0.65 parts per Billion device hours at 55 degC. This report can be found from the landing page on
www.analog.com.
So 0.65 failures per billion device hours is 1,538,000,000 hours per failure (taking the reciprocal of 0.65/1Billion). Divide this by (24 x 365) to give years per failure (or mean time between failures, MTBF) = 175,000 years.
So, at 55 degC you can run a part for 175,000 years before it will statistically fail.
At 125 degC, this goes down to 2,250 years.
So although, as temperature goes up, so do silicon failures, the numbers are minuscule.
However, as temperature goes up, mechanical and chemical problems start getting worse and these are far far more likely to cause a circuit to malfunction compared with anything dictated by Arrhenius.
I continue this argument in another comment (see below)....