MTTF calculator
MTTF is the mean of the life distribution — the average time to failure if every unit is run to death. For two-parameter Weibull it is not characteristic life η and it is not B10. Use it for expected energy, spares at the mean, or comparison to an exponential baseline; use B-lives when you care about a failed fraction.
Open the Weibull.Genie workbook Open Weibull Calculator Compute mean life from a fit
Formula
MTTF = E[T] = η Γ(1 + 1/β)
The exponential special case is β = 1: Γ(2) = 1, so MTTF = η. That is the only shape where “characteristic life” and “mean life” coincide. Weibull.Genie keeps both on the calculator so they cannot be confused.
Worked example (β = 2, η = 1 000 h)
Shape 2 is a clean wear-out Weibull (Rayleigh). Then 1 + 1/β = 1.5 and
MTTF = 1 000 × Γ(1.5) = 1 000 × √π / 2 ≈ 886 h
| Name | What it is | β = 2, η = 1 000 h |
|---|---|---|
| B10 | 10% failed quantile | 325 h |
| Median B50 | 50% failed quantile | 833 h |
| MTTF | mean E[T] | 886 h |
| η | 63.2% failed (scale) | 1 000 h |
Open Weibull Calculator → Mean life after a workbook fit. The bearing-sample MLE (β ≈ 2.17, η ≈ 716 h) has MTTF ≈ 634 h — again below η, as wear-out requires. Related: B10 life and hazard rate.
FAQ
What is MTTF for a Weibull distribution?
Mean time to failure is the expected life: MTTF = η Γ(1 + 1/β), where Γ is the gamma function. It is the mean of the distribution, not a reliability quantile such as B10.
When does MTTF equal η?
Only when β = 1 (exponential). Then MTTF = η = 1/λ and the hazard is constant. For wear-out (β > 1) MTTF is less than η; for infant mortality (β < 1) MTTF is greater than η.
Is MTTF the same as MTBF?
MTTF is for non-repairable items (time to first failure). MTBF is for repairable systems (mean time between failures). Weibull.Genie is a life-data workbook for units that fail and are suspended — it reports mean life MTTF from the fitted LifeFit, not a repairable-process MTBF.
Where is mean life in Weibull.Genie?
Fit the grid on the Weibull Workbook, then Weibull Calculator → Life → Mean life. Mean remaining life at age T is also there; at T = 0 it matches MTTF.