MTTF and MBTF
MTBF
Mean time between failures (MTBF) can be summarized as
\[\frac{total\ operational\ time}{total\ number\ of\ failures}\]Or, more precisely,
\[\frac{\sum(start\ of\ downtime - start\ of\ uptime)}{total\ number\ of\ failures}\]MTTF
Mean time to failure (MTTF) applies to items that cannot be repaired and is basically the lifetime of an object. It can be summarized as
\[\frac{\text{total hours of operation}}{\text{total number of units}}\]which is equivalent to
\[\frac{(time\ period)*(number\ of\ items\ tested)}{number\ of\ items\ that\ failed\ within\ the\ time\ period}\]In practice
Current SSD drives have an MTBF of 1.5 million hours. One year has 24*365=8760 hours. This means that if we had 1000 hard disks running 24/7 we can expect 1_000 * 8_760 / 1_500_000 = 5.84 disk failures.