Hi Johnny
The reliability of a system (however you define that system) is the probability of a failure occuring within a defined period of time.I'm sorry but the definition of reliability means you have to use the equation that calculates it from MTBF and time. There may be different ways of expressing the equation but at the end of the day it's always going to be the same equation. Why do you want/need to use another equation?
-(time/MTBF)
Reliability = e
Everything fails eventually, so given a long enough 'time' everything's reliability is zero. Equally, if you reduce the 'time' to a small enough period you can achieve a seemingly impossible 100% reliability for anything. It's up to the user to use an appropriate period relevant to their needs e.g. 1 month, 1 year etc.
Regards
Ken