No stats, but way back in the day of very large computers (1 each) in very large facilities, it seems like the thing we worried most about at restart was too-rapid cooling and the resulting condensation if the conditions were right.
After power-up the next thing was disk crashes that occurred on the way down (this was a long time ago discs and drums are different now).
Lastly was overheat failures which were relatively few and always in components with a weakness reputation.