Weibull is the extreme-value type III: limit distribution for the MIN of iid samples with a lower bound. It is the Exponential's hazard-tunable cousin and the workhorse of reliability engineering.
β Intro Β· expand
Try first (productive failure)
Before the worked example: spend 60 seconds taking your best shot at this.
A guess is fine β being briefly wrong about a problem makes the explanation
land harder when you read it. This appears once per tutorial; skip
if you already know the trick.
60s
β Try first Β· expand
Worked example
A turbine bearing has time-to-failure T modelled as Weibull with shape k = 2 and scale Ξ» = 10 (years). The Weibull CDF is F(t) = 1 - exp(-(t/Ξ»)^k) for t β₯ 0. (a) Identify the hazard-rate behaviour. (b) Compute P(T > 5). (c) Compute the median. (d) Compute the mean E[T] = Ξ» Ξ(1 + 1/k).
β Worked example Β· expand
Practice 1 of 3Type a fraction, decimal, or expression β mathjs parses it.
β Practice Β· expand
Reflection
Where does this distribution sit in the story chain β what question does it answer that the previous distribution couldn't? Try to recall the key moment formulas (mean, variance) without looking them up.
