Fatigue Failure Models ߝ Birnbaum-Saunders vs. Inverse Gaussian

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Abstract
The assumption of a common underlying failure process leads to both the inverse Gaussian distribution and the fatigue life distribution of Birnbaum & Saunders. The first is obtained by an exact derivation while the second involves certain approximations. Although both of these distributions fit many failure data well, the inverse Gaussian distribution enjoys a distinct advantage in regard to the availability of procedures for a sound statistical analysis and tractability of the sampling distributions.