Cirteria for Random Vibration

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 Steinberg says: Since 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