MTTF could be defined as the expected value of the function of the statistical distribution of failures, which is ∫t f(t)dt;
assuming that the distribution of failure is approximated by the exponential distribution (that means having a failure rate constant in time),
the MTTF could be approximated by the reciprocal of the failure rate λ.
again, failure rate for a system, under some approximations, can be obtained testing the component and adding number of failures / time of testing
so MTTF = time in service / number of failures