A lot of Western aviation qualifying authorities specify a maximum allowable mean time between failure (MTBF) of 1 per 100000 flight hours. I imagine most rocket engine designs would be more like one per hour! That said, they only have to operate for about ten minutes though before they are disposed of, in the case of expendable launch vehicles.

In Falcon 9's case, and totally from memory and probably incorrect and very approximate, we've had 4 launches, each has had 9 Merlin C engines on the first stage, the first stage burn time is 170s or about 3 minutes. There have been two failures - a non destructive engine shutdown on the previous ISS mission on the pad at T-very_little, and the rather more messy rapid disassembly failure of something near the engine or the engine itself on the most recent launch.

So, for this first stage engine the MTBF (remember this is all a bit silly and inaccurate and just for ballpark comparisons with the airline industry) the MTBF has been:

9(engines/launch)4(launches)0.05(3 min burns in hours)*0.5(2 failures) = 0.9, i.e. a MTBF of 55 minutes for Merlin 1C lower stage, vs most regulators requiring mtbf > 100000 hours on commercial jet airliner engines.

So there's a bit of a way to go yet!