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.
They're not saying, "commercial jet engines are more reliable; therefore we should use them". The issue is that the Merlin 1C engine simply hasn't had enough flights to build up its denominator.
It doesn't make sense to normalize for thrust here. This is just failure rate. There's nothing wrong with having a comparatively high failure rate when the sample size is several orders of magnitude smaller: the statistical significance is just weaker; we acknowledge that and move on.
Here's a 1993 paper giving MTBF failures for the space shuttle's main engine. With some improvements that the author of the paper suggests, it looks like MTBF is about one per 254 flights at 100% power and one in 139 flights at 104% power . (It drops to one in 20 flights at 109% power! It's surprised the failure rate has such a strong dependency on power output --- the relationship suggests that failures have something to do with thermal stress.)
It's interesting to compare that MTBF with the fact that there are about ten million airliner flights per year in the US. If we arbitrarily assume that the average airliner flight is two hours, that's a substantial number of failed engines per year, so obviously the redundancy on these craft really does work.
Incidentally, I went searching for airliner engine MTBF statistics and your comment was already near the top of Google's results.
Edit: erroneously said five million flights per year because I was looking at 2012 statistics for only the first six months. of the year. Oops.
Ah yes, good stuff. I forgot about the aborted launch, and the initial Falcon 9 launch without Dragon. My 1/27 figure, in addition to being overly simplistic, is wrong.
