Weibull distribution mean: MTBF = η · Γ(1 + 1/β). Useful when β ≠ 1 (wear-out or infant-mortality).
Formula
$$ \text{MTBF} = \eta \cdot \Gamma!\left(1 + \tfrac{1}{\beta}\right) $$
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $η$ | Weibull scale | h | MLE fit |
| $β$ | Weibull shape | - | MLE fit |
| $Γ$ | Gamma function | - | Lanczos approx |
Sources
- Abernethy - The New Weibull Handbook.