A graph of stress versus lifetime constitutes one of the first attempts to quantitatively examine fatigue lifetimes. This graph, introduced by August Wöhler in 1858, has since become known as the S-N curve. Although the S-N plot provides an estimate of lifetime for a given stress level, it does not take into account any estimate of uncertainty. S-N-P plots are a probabilistic modification which give an estimate of probability of failure, conditional on number of cycles and stress level.
It should be noted that this is very much an empirical method in the sense that the only variables are time and stress. Calibration of such curves are done by experiment, using test specimens.
Another common method of estimating lifetime consists of fitting the parameters of a Weibull distribution from test data, and this can yield good predictions in practice.