Failure Rate Versus MTTF
If the failure rate of a system or item follows the exponential distribution, then the failure rate can be calculated as the reciprocal of the MTTF (mean time to failure). In other cases, MTTF cannot be calculated in this way because failure rate is a time-varying function (whereas MTTF is a time-independent function). At the same time, we cannot use the reciprocal of average failure rate over a given time to compute MTTF.
In fact, if failure rate is an increasing (decreasing) function, then the average failure rate over zero and infinity becomes infinity (zero) unless the failure rate as time tends to infinite is finite and non-zero. This means, even for non-exponential cases, it is not necessary to have a linear relation between failure rate and MTTF. In other words, the correct relationship between MTTF and failure rate λ(t) is: