Birnbaum–Saunders distribution

The jth cycle leads to an increase in the crack by Xj amount.

The probability that the crack does not exceed a critical length ω is where Φ() is the cdf of normal distribution.

The mean (μ), variance (σ2), skewness (γ) and kurtosis (κ) are as follows: Given a data set that is thought to be Birnbaum–Saunders distributed the parameters' values are best estimated by maximum likelihood.

The case where μ = 0 and β = 1 is called the standard fatigue life distribution.

This article incorporates public domain material from the National Institute of Standards and Technology