Annualized failure rate (AFR) is the relation between the mean time between failure (MTBF) and the hours that a number of devices are run per year, expressed in percent. AFR does not specifically apply to a single component, but rather to a population of like components. To quote Seagate "AFR and MTBF are population statistics that are not relevant to individual units." ^{[1]}
MTBF should not be confused with useful life. The useful life of a component predicts how long a single component may be reasonably used. MTBF is a measure of the component's reliability whilst it is functioning within its useful life. A component may have a useful life of only a couple of years, and the same component may well have a MTBF of hundreds of years (e.g. disks). The MTBF does not imply how long the component may be usefully used for.
For a component with "constant failure rate", the proper form for AFR is given as:
AFR = 1 − exp( − AnnualO H / MTBF)
Where
AFR = Annualized Failure Rate [Fraction]  This can be easily converted to % MTBF = Mean Time Between Failure [hours] AnnualOH = Annual Operating Hours [hours]  this is usually 8760 hours (24*365), but can be different
However, when MTBF >> AnnualOH, the following formula is a good approximation
AFR = AnnualO H / MTBF
or with continuous operation
AFR = 8760 / MTBF
The above formula is far easier to use, and is often quoted as the only correct form. However, this can be easily shown to be false by taking a simple example of
MTBF of 5,000 hours, and a population of 100 disks constantly in use. Using the approximate form for AFR one might expect 175 disks to fail within a single year's operation, when the true answer cannot be larger than 100. It is actually closer to 83. Thus MTBF of 5,000 hours is equivalent to AFR of 83%.
Conversley, taking MTBF to be 50,000 hours, and a population of 100 disks constantly in use. Using the approximate form, 17.5 disks are expected to fail; the full exponential formula gives 16, which is close enough. Thus MTBF of 50,000 hours is equivalent to AFR of 16% (or 17.5%).
The above two examples also demonstrates the concept of how MTBF and AFR should be applied to populations, and not to individual components
A disk drive's MTBF number may be 1,200,000 hours and the disk drive may be running 24 hours a day, seven days a week^{[2]}. One year has 8,760 hours.
then take the reciprocal of 136.9863 years
You can expect about 0.73 percent of the population of these disk drives to fail in the average year.
Another example: A disk drive's MTBF number may be 700,000 hours and the disk drive may be running 2400 hours a year^{[3]}.
then take the reciprocal of 291.6667 years
You can expect about 0.34 percent of the population of these disk drives to fail in the average year.
Now assuming you let the same disk run 24 hours a day, 7 days a week:
then take the reciprocal of 79.9087 years
You can expect about 1.25 percent of the population of these disk drives to fail in the average year.
Field Results Moving away from manufacterers accelerated fatigue life results for AFR the following paper gives infield measurements of disks failures and resulting AFR (and thus MTBF) ^{[4]} page 4, figure 2 and subsequent figures
