# Glossary

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RAID          -- Redundant Array of Inexpensive Disks

MTTF         -- Mean-Time-To-Failure

Average interval of time that a component will operate before failing. See Failure Functions below.

MTTR         -- Mean-Time-To-Repair

Average amount of time needed to repair a component, recover a system, or otherwise restore service after a failure. See Failure Functions below.

MTBF         -- Mean-Time-Between-Failures

MTBF = MTTR + MTTR

MTTDL       -- Mean-Time-To-Data-Loss

A reliability metric. MTTDL is a function of MTTF, MTTR, total number of disks in the system (N), and parity group size (G).

Failure Functions.

When a time basis is determined, failures can be expressed in several ways: the cumulative failure function, the failure intensity function, the failure rate function, and the mean time to failure function. The cumulative failure func- tion (also called the mean value function) denotes the average cumulative failures associated with each point of time. The failure intensity function represents the rate of change of the cumulative failure function. The failure rate function (or called the hazard rate, or the rate of occurrence of failures) is defined as the instantaneous failure rate at a time t, given that the system has not failed up to t. The mean time to failure (MTTF) function represents the expected time that the next failure will be observed. (MTTF is also known as MTBF, mean time between failures.) Note that the above three measures are closely-related and could be translated with one another.

Mean Time To Repair and Availability. Another quantity related to time is mean time to repair (MTTR), which represents the expected time until a system will be repaired after a failure is observed. When the MTTF and MTTR for a system are measured, its availability can be obtained.

Availability -- is the probability that a system is available when needed. Typically, it is measured by

MTTF
Availability  =  -----------
MTTF + MTTR

ECC            -- Error Correction Code

BER            -- Bit Error Rate

p(disk)        -- The probability of reading all sectors on a disk (derived from disk size, sector size, and BER)

G                 -- parity group size i.e., number of disks in parity group

N                 -- total number of disks in a redundant array system

seek time     -- Amount of time needed to move the head to the correct radial position of the disk.

rotational latency -- Amount of time needed for the desired sector to rotate under the disk head.