I think this is an interesting question from an operations research / simulation exercise. As such you could attack the question very simply to start with and then go on more and more detailed if it makes sense. Not very different really from many other OR questions.
A very first, very simple calculation can be done on the back of an envelope, say per week:
- each week of flights creates $x$ dollars in profit per plane.
- each plane set aside as spare costs $y$ dollars.
- one problem takes $z$ weeks to fix.
- the probability of a plane getting a problem needed to be fixed is $p$.
You can now calculate an optimum where (profit) - (costs for spare planes) is at maximum.
My guess though, is that the cost to keep a plane as a spare is high, and the profit per week is low, giving a profit maximum at $0$ spare planes.
Starting from this very simple back of the envelope calculation you can start adding details. Maybe it takes different amounts of time to fix the plane (with different probabilities). Maybe, even if you have a plane it is in the wrong airport so you will miss a few of the flights. Maybe you could rent a plane for a while. And on it goes. My guess is that rather soon you find that there are several stochastical variables and that the analytical answer will be difficult to find -- you then start doing simulations instead.