A methodology to determine a conditional probability density distribution surface from S–N data

A conditional probability density distribution surface (CPDDS) is constructed by two functions in this paper. One is the function of population mean and the stress level; the other is the function of standard deviation and the stress level. The surface represents the probability density curve of fatigue life changing with the stress level. A new definition of fatigue limit as well as the determination method is given in this paper according to the small probability event of CPDDS. The proposed method can save considerable cost and time in the determination of fatigue limit.

► We model a conditional probability density surface based on the conditional probability.
► We proved the existence of the surface by two high-cycle tests.
► The surface expressed the fatigue properties such as the fatigue life distribution, the fatigue limit and the p–S–N curve.
► The fatigue limit is determined by the small probability event of the surface and avoids the staircase method.
► This research may be an exploration of a new method to study the fatigue properties.