MTBF is the arithmetical mean of the time between a number of failures of a single system or device, or all failures of a population of similar systems or devices. There are a variety of ways people choose to calculate MTBF and many are driven by the availability of information. Often, the MTBF is the time between successive failures. For some people, the MTBF is the time from the end of the last repair to the next failure. For others, the time in operation can be calculated accurately.
The best approach is the one that takes into account the time the device is exposed to all forms of deterioration that will ultimately contribute to the next failure.