Hair Breakage 268 In fatigue testing, a common analysis approach involves fitting a Weibull distribution to the data.6 The advantage of a Weibull distribution is its flexibility, in that it can be used to describe a wide variety of data. The cumulative form of the Weibull equation is: Where F(x) is the probability of the fiber breaking in x cycles, α is the characteristic lifetime at which 63.2% of the fibers have broken, and β is the shape factor. The flexibility of the expression is provided by the Weibull shape factor, β. That is, when β = 3.6, the Weibull function approximates the normal distribution whereas, when β = 1, the distribution is equivalent to the exponential distribution. As such, the above expression can be used to model a wide variety of data, which is subsequently described by evaluation of the two Weibull parameters. Figure 12. Histogram of cycles-to-fail for Caucasian hair at 60% RH under a repeating 0.010-0.011 g/um2 stress