How is reliability related to MTBF?

With a constant failure rate, R(t) = e^(−t/MTBF). So at t = MTBF reliability is only 37%, not 50% — MTBF is a rate, not a guaranteed lifetime.

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Reliability / MTBF

With a constant failure rate, reliability decays exponentially: R(t) = e^(−t/MTBF). Series parts multiply (all must survive); redundant parallel parts add reliability (only one must survive). Availability folds in repair time.

Single item

MTBF (hours)

Mission time t (hours)

Reliability R(t)

—

System of equal blocks

Config

Number of blocks

System R

—

Each block uses the MTBF and mission time above. Series R = Rⁿ; parallel R = 1−(1−R)ⁿ.

Availability & Weibull

MTTR — mean repair (hours)

Weibull η (scale, hours)

Weibull β (shape)

Availability

—

Weibull R(t)

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Weibull β<1 = infant mortality, β=1 = random (exponential), β>1 = wear-out.

Reliability over time

■ exponential R(t)=e^(−t/MTBF) ■ Weibull. The dashed line is your mission time — note R at one MTBF is 37%, not 50%.

Constant-failure-rate model unless using the Weibull field. A helper, not a substitute for engineering judgment.