Weibull Distribution Calculator

How it works

F(x) = 1 − e^(−(x/λ)^k); R(x) = e^(−(x/λ)^k); f(x) = (k/λ)(x/λ)^(k−1)·e^(−(x/λ)^k); h(x) = (k/λ)(x/λ)^(k−1); mean = λΓ(1 + 1/k); median = λ(ln 2)^(1/k); B10 = λ(−ln 0.9)^(1/k)

The Weibull distribution is the workhorse of reliability engineering and survival analysis, and also models wind speeds and particle sizes. The shape k sets how the failure rate changes over time: k < 1 means early “infant-mortality” failures, k = 1 a constant rate (the exponential distribution) and k > 1 wear-out. The scale λ is the characteristic life — the time by which 63.2% of units have failed. Formulas follow the NIST/SEMATECH e-Handbook.

Worked example

With shape k = 1.5 and scale λ = 1,000 hours, the probability that a unit has failed by 500 hours is 0.2978 and its reliability is 0.7022; the mean life is 902.7 hours, the median 783.2 hours and the B10 life is 223.1 hours.

Sources: NIST/SEMATECH e-Handbook — Weibull distribution · NIST/SEMATECH e-Handbook — Reliability: Weibull

Frequently asked questions