A Statistically Load-Weighted Probabilistic Fatigue Life Model
By interpreting traditional stress-strength interference model as a statistical average of the probability that strength (a random variable) is greater than stress (another random variable) over its whole distribution range, the same model configuration, which was conventionally applied only to the case of same system-of-units parameters (e.g., stress and strength, both are measured in MPa), was applied to more general situation of different system-of-units parameters. That is to say, the traditional model was extended to more general situations of any two variables, as long as one of the variables can be expressed as a function of the other. Further more, the probabilistic fatigue life under random stress can be predicted, with known probabilistic fatigue lives under several deterministic cyclic stress amplitudes and known distribution of the random cyclic stress amplitude. The underlying principle is that the fatigue life under random stress is equal to the statistical average of the fatigue lives under cyclic stress of deterministic amplitudes which can be considered as the samples of the random stress.
Z.Y. Shen, M.N. James, W.D. Li, and Y.X. Zhao
L. Y. Xie and W. Q. Lin, "A Statistically Load-Weighted Probabilistic Fatigue Life Model", Advanced Materials Research, Vols. 44-46, pp. 51-56, 2008