planemad2,
I like you logic, but it is flawed...
The 146/RJ has been flying for much more time than the 777, basically only AlliedSignal & Lycoming as engine manufacturer for the 146/RJ family, you have multiple for the 777 (GE/PW/RR).
For each flight hour a 146/RJ does, it adds 4 hours to the number of hours the engine type has done in service. Similar, each flight hour a 777 does, it adds 2 hours to the number of hours the engine type
for that manufacturer has done in service.
Now the mean time between failure (MTBF) is defined as
MTBF = (flying hours * aircraft quantity)/(number of confirmed failures)
The 777 has had a number of engine failures, can remember high speed rejects, inflight, and even the 777 demostration a/c in south africa have had failures. Its a new engine, has not flown a lot relative to the 146/RJ. A new engine is prone to more teathing problems than a proven engine.
So IMHO the MTBF on a 777 would be higher than that of a 146, purely because the maturity of the 146/RJ fleet, and the 4 times factor per flight hour vs 2 (maybe less if you consider the 3 777 engine manufacturers), the maturity of the engine, and the single engine manufacturer for the aircraft.
However, I do see the 777 MTFB to increase, and the 146/RJ one to stay static or decrease.