Weibull analysis calculator (β, η, B-life)

The Weibull distribution describes the nature of failures with a single number, the shape parameter β. β < 1 means infant mortality, where the failure rate falls over time as manufacturing defects show up; β ≈ 1 means random failures at a constant rate; β > 1 means wear-out, where the failure rate rises over time. These map directly onto the three regions of the bathtub curve.

In semiconductors, lifetime data for gate oxide breakdown (TDDB), electromigration and thermal fatigue of solder joints are plotted on Weibull paper. The β of TDDB depends on oxide thickness: thinner oxides have smaller β and a wider spread of failure times, which makes lifetime guarantees for ultrathin films difficult.