I would recommend "Vibration Analysis for Electronic Equipment" by
Steinberg. I don't work with EE stuff, but it's the best text I've
found for random vibe analysis.
This is essentially what SteSince the input is random, one can assume that the resulting stresses
are normally distributed. Therefore, the stress you get from your
model is considered the "1-sigma" stress level. This stress would
occur 68.3% of the time (assuming a normal dist). The 2-sigma
stresses are 2 times your 1-sigma stress, and occur 27.1% of the time.
And finally, the 3-sigma stress is obviously 3 times the 1-sigma
stress, and occurs 4.3% of the time. As a first pass, you can assume
that the 3-sigma stresses occur 100% of the time. If you pass with
positive margins (using Goodman, for instance), then you're good. If
you don't pass, then you can break your cycles down into the 1-, 2-,
and 3-sigma components and sum up your damage using Miner's Rule.
Hope this helps