G,
At design phase there is a theoretical constant MTBF, this is how Boeing was able to get the 777 ETOPS approved "off the plan" without flying for the normal surveillance period. Previous to the 777 ETOPS approval from the FAA required operators to establish the systems and documentation for a period of time and report any failures during that period.
The MTBF in real life varies as engine trend monitoring equipment and trip logs are collected, either manually or via some electronic means like ACARS, quick access recorders etc, and is used to build a statistical picture.
The actual MTBF is not a constant, and varies between operators, we can see here in Australia that
VB do not have automatic rights to the same ETOPS planning as what QF does for their 737's. Does this mean a
VB 737 is more likely to have an engine failure than a QF one, no. However QF has a more substantial set of historical statistical data they can draw on, and hence a lower MTBF, this is due to flying more hours with the engine type.
What really determines the MTBF is the number of hours the engine flies, a 4 engine aircraft build this statistical picture up quicker than a 2 engine aircraft, and generally also fly longer routes, with less cycles, which all aids in reducing the actual MTBF.
The formula you have illustrated fails to take in account that the actual MTBF is not a constant, it can only be used to look at a snapshot of data. It was however a nice twist to a dull discussion.
P.S. you must be a gambling man...your formula looks a lot like the \'Fundamental Formula of Gambling\' (FFG): N = log(1 – DC) / log(1 - p).......
