This happens if there is an “aging” process e.g. A value of β 1 indicates that the failure rate increases with time.If x represents “time-to-failure”, the Weibull distribution is characterized by the fact that the failure rate is proportional to a power of time, namely β – 1. Click here for more information about this version. Observation: There is also a three-parameter version of the Weibull distribution. Thus, the inverse cumulative distribution function is Solving for x results in x = α(-ln(1- p)) 1/ β. Taking the natural log of both sides, we get ln(1 – p) = -( x/ α) β. The cumulative distribution function (cdf) is Here β > 0 is the shape parameter and α > 0 is the scale parameter. Definition 1: The Weibull distribution has the probability density function (pdf)įor x ≥ 0.
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