While it gives a good indication of some of the factors in play, that's an old formula which
(a) does not include the load life-rating
(b) does not account for the effects of ripple current.
It uses a testing-time duration fudge factor instead of the modern fudge factor for lifespan estimation.
The more modern formula used by CDE and IC (same company now, I think), among others, is:
Given:
// Capacitor Parameters
L1 = Load life rating
L2 = Operating Life at temperature Ta
Vr = Rated voltage
Tm = maximum rated temperature
// Environmental Parameters
Vo = Applied voltage
Vr = Ripple voltage
Ta = Ambient temperature
Tr = Temperature rise due to ripple current
Then:
L2 = L1 x (Vr / Vo) x 2^[(Tm - (Ta + Tr)) / 10]
You can see how as
Ta approaches
Tm the lifespan drops, and how as it moves away from
Tm the lifespan increases. But what is key here is that the ripple current heating,
Tr, is also reducing lifespan. So, all other factors being within specification, even if the ambient temperature is not high, the ripple current heating can destroy the capacitor. This is one of the secrets of power supplies.
The problem with gauging lifespan for older capacitors is that the materials degrade when not used. The kraft paper used in PIO, for example, began life as ground up trees. The treatment process left behind acidic residue which degrades the paper and the metal components, and the oils used were vegetable (typically castor oil or other vegetable oil) which polymerize over time and the ESR climbs. The more oxygen gets in, the worse it is. This is why the quality of the vent, poor in the old days, matters. If the plus is natural rubber it leaks. This problem, BTW, continues to exist. Many of the counterfeit capacitors use natural rubber or latex plugs instead of silicone, elastomer, or other synthetics. Over time the plug hardens and shrinks, and this permits the entry of air and the evaporation of electrolyte.
The dielectric absorption (DA) for older capacitors is very high, so electrons migrate into the dielectric and then slowly migrate out when the field is reversed. This averages the signal being applied to the capacitor with its signal history. Something most proponents of older capacitors simply do not understand. This is why A/D and D/A circuitry requires capacitors with low DA. The DA issue, BTW, can injure or kill with a high-voltage capacitor. Even though voltage has been removed and the capacitor "discharged", some charge remains and it gradually leaks out. This is why capacitors are stored with a wire across the terminals. It prevents any danger from residual charge.
Modern capacitors from CDE, IC, etc. are rated for a maximum lifespan of about
15 years. So the "theoretical" lifepsan of 50+ years is nonsense. A change in value of 20% or greater is deemed to be failure, so definitional issues may account for the difference, but I think it was a lack of knowledge. Old capacitors have no Magickal Mojo, they just have high ESR, high DA, high distortion, poor tolerances, and materials prone to fail.
Eh. This was probably more than anyone wanted to read.