There are two parts to deal with uncertainty in fatigue design: determining the distributions of possible values for all uncertain inputs and calculating the probability of failure due to all the uncertain inputs. This article discusses the sources of uncertainty in a fatigue analysis, such as the material properties, distribution of applied stress levels within a given environment, environments or loading intensities, and modeling or prediction. It presents a probabilistic approach for analyzing the uncertainties and determining the level of reliability (probability of failure).
Paul S. Veers, Statistical Considerations in Fatigue, Fatigue and Fracture, Vol 19, ASM Handbook, By ASM Handbook Committee, ASM International, 1996, p 295–302, https://doi.org/10.31399/asm.hb.v19.a0002369
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