  This article addresses the probabilistic nature of fatigue life in structures
subjected to cyclic loading with variable amplitude. Drawing on the
formalisation of Miner's cumulative damage rule that we introduced in the
recent article [Cartiaux, Ehrlacher, Legoll, Libal and Reygner, Prob. Eng.
Mech. 2023], we apply our methodology to estimate the survival probability of
an industrial structure using experimental data. The study considers both the
randomness in the initial state of the structure and in the amplitude of
loading cycles. The results indicate that the variability of loading cycles can
be captured through the concept of deterministic equivalent damage, providing a
computationally efficient method for assessing the fatigue life of the
structure. Furthermore, the article highlights that the usual combination of
Miner's rule and of the weakest link principle systematically overestimates the
structure's fatigue life. On the case study that we consider, this
overestimation reaches a multiplicative factor of more than two. We then
describe how the probabilistic framework that we have introduced offers a
remedy to this overestimation.
