# Annualized failure rate

Annualized failure rate (AFR) gives the estimated probability that a device or component will fail during a full year of use. It is a relation between the mean time between failure (MTBF) and the hours that a number of devices are run per year. AFR is estimated from a sample of like components—AFR and MTBF as given by vendors are population statistics that can not predict the behaviour of an individual unit.[1]

## Hard drives

For example, AFR is used to characterize the reliability of hard disk drives.

The relationship between AFR and MTBF is:[1]

$AFR = 1-exp(-8760/MTBF).$

This equation assumes that the drives are powered on for the full 8760 hours of a year, and gives the estimated fraction of an original sample of drives that will suffer from disk failures, or, equivalently, 1 − AFR is the fraction of drives that will show no failures over a year. It is based on an exponential failure distribution (see Failure rate for a full derivation).

This can be approximated by, assuming a small AFR,

$AFR = {1 \over {MTBF / 8760}} \cdot 100$ (expressed in %).

For example, a common specification for PATA and SATA drives may be 300,000 MTBF, giving a theoretical 2.88% annualized failure rate i.e. a 2.88% chance that a given drive will fail during a year of use.

The AFR for a drive is derived from time-to-fail data from a reliability-demonstration test (RDT).[2]

AFR will increase towards and beyond the end of the service life of a device or component. Google's 2007 study found, based on a large field sample of drives, that actual AFRs for individual drives ranged from 1.7% for first year drives to over 8.6% for three-year old drives.[3] A CMU 2007 study showed an estimated 3% mean AFR over 1–5 years based on replacement logs for a large sample of drives.[4]