Does the FAA have risk targets for specific activities? Does the FAA have or publish goal values for various risks?

I'm looking for something that says (e. g.) "We rate passenger airline flights as 'safe' if there are fewer than X casualties per million flying hours" or the like.  Even better would be some kind of matrix reflecting "safe", "of concern", "hazardous", "dangerous", etc.
"We rate passenger airline flights as 'safe' if there are fewer than X casualties per million flying hours"

I am not aware of any official FAA document that states such sentence. However, something similar can be deduced from safety requirements related to the development of aviation systems. 

ARP4761 is a well-known standard for conducting safety assessments on civil airborne systems and equipment. A probability of failure occurrence associated with the severity classification can be found on page 14, which shows the following table:



As it can be seen, the maximum allowed occurrence of a catastrophic failure is 1.0E-9. Playing a bit with the numbers, this could be translated in:


  Commercial aviation flights are considered as 'safe' if there are fewer than 1 catastrophic condition per billion flight hours


One could assume that a catastrophic condition can lead to fatalities, and this seems reasonable. But I'm afraid that this presumption is not written in official FAA publications (I might be wrong).



P.D.: Now, where these probabilities of occurrence come from is another interesting (and un-official) story, but I think is out of the scope of this question for the moment.