What percent of crashes are due to bicycle failure? I find myself avoiding steep/fast downhills. Not because I'm afraid I'll lose control, but because something might happen to my bike that will send me face-first into the pavement.

Are there any statistics on this?

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By "crash due to bicycle failure", I mean a crash that would not have happened if something hadn't happened to the bicycle. This would include, for example, pounding your bike over bumps, resulting in the stem breaking. This would not include losing control because you pounded your bike over bumps.

By "crash", I mean an accident serious enough to be documented. If you fall over at a stoplight because you couldn't unclip, that obviously won't be documented and therefore doesn't count as a crash.
There are some statistics available from Great Britain for Contributory factors for reported road accidents. Below are the 2014 figures for Pedal Cycles, the first column is number and the second is percent.



Note that only reported accidents where a police officer attended the scene are included in the statistics. This Wikipedia article has some details of the methodology used to collect the statistics.

The complete data set is available here. The data above is taken from the table RAS50005 - Vehicles in reported accidents by contributory factor and vehicle type, Great Britain, 2014.