When a geosynchronous/geostationary satellite is launched, how do its designers calculate its life expectancy? A random sampling of some communication satellites suggest that ~ten years might be the norm. How is this figure arrived at? Is it simply a question of propellant required for orbital corrections and eventual retirement to a graveyard orbit?
Typically propellant consumables for station keeping were the limiting factor. Once a Geosat reaches near the end of its propellant life, they need to maneuver it out of GEO so as to free up the slot for its replacement.
This has been mitigated somewhat by the use of electric propulsion, where Xenon or the like is used as propellant after being accelerated electrically for thrust. The propellant in that case is much smaller in quantity due to the higher ISP but lower thrust. I.e. If you use a low thrust very high ISP system, and have lots of time, it is more efficient long term.
Solar panels used to degrade and power was thus reduced to the point where it could no longer function. (Or conversely, knowing how fast the panels would degrade, they would launch oversized panels, so that in 10 years, degraded it would still have enough power to operate). Better panels have mitigated that somewhat.
If there are strong pointing requirement, reaction control wheels (gyros) are well known failure points, since by definition they are moving parts. (Kepler, Hubble, ISS, etc are examples where issues have come up).
Electronics exposure to radiation in space, outside the Van Allen belts can degrade the electronics, but mostly this has been mitigated with better shielding and electronics.
To calculate life expectancy, there are a few things to consider. The first is to determine how long we want it to last, as this is going to drive other considerations. As the launch cost is a considerable part of the investment, one aims to maximize the lifetime, taking all other considerations into account. To be sure the satellite lives as long as we want it to, a reliability analysis is performed, taking into account everything that can fail. From that the amount of spare units to fly (doubling essential units, flying 5 amplifiers when 3 are used for normal operation etc, etc).
The second important element is the fuel budget. At launch, about half the satellite mass is fuel, considering a chemical propulsion system. Of this by far the biggest part is used to bring the satellite from its transfer orbit (which is achieved by the launch vehicle) to the geostationary orbit. The fuel budget covers a number of uncertainties (accuracy of the transfer orbit, efficiency of orbit raising maneuvers). If the fuel allocated for these uncertainties is not used, it becomes available for all other tasks and typically extends the useful lifetime beyond the design life of the satellite.