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MTBF, MTTR and availability

MTBF (Mean Time Between Failures) is the average time between failures, while MTTR (Mean Time To Repair) is the average repair time. Availability is the fraction of time the system actually works, and increases with higher MTBF and lower MTTR. For a constant failure rate, the failure rate $\lambda$ is the inverse of MTBF.

A = \frac{MTBF}{MTBF + MTTR}

availability

\lambda = \frac{1}{MTBF}

failure rate with constant failure rate

Symbols

$MTBF$	average time between failures	h
$MTTR$	average repair time	h
$A$	availability, fraction of time

Example

MTBF $= 5000$ h, MTTR $= 2$ h:

$A = 5000/5002 \approx 0.9996$ , i.e. 99.96% uptime.

Availability near 1 requires either very high MTBF or very low MTTR — ideally both.

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Part of Statistics and Risk Analysis: Inference and risk.