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Weibull MTBF

Weibull distribution mean: MTBF = η · Γ(1 + 1/β). Useful when β ≠ 1 (wear-out or infant-mortality).

MaintenanceWeibull

Scale ηhShape β - β<1 infant mortality; β=1 constant rate; β>1 wear-out. Bearings β≈2–3; gears β≈3–4.

Γ(1 + 1/β)

0.8873 -

MTBF

4,436h

Formula, assumptions, and limits

η and β typically fit from failure-time data (median-rank regression or MLE). β < 1 indicates a population with infant mortality - burn-in helps. β > 1 indicates wearout - scheduled replacement makes sense.

Symbol legend

Meaning	Unit	Source
Weibull scale	h	MLE fit
Weibull shape	-	MLE fit
Gamma function	-	Lanczos approx