Normally I would try and find systematic risk analyses by people who know more about this subject than me. However, Martin Hellman has written a preliminary risk analysis of nuclear deterrence as part of his Defusing the Nuclear Threat project, and he claims that there have been no formal studies of the failure rate of nuclear deterrence. Hellman himself estimates that failure rate as on the order of 1% a year, but I don't know how seriously to take that estimate.