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Uncertainty in modeling the fatigue life of a full-scale component using experimental data at microscopic (Level 1), specimen (Level 2), and full-size (Level 3) scales, is addressed by applying statistical theory of prediction intervals, and that of tolerance intervals based on the concept of coverage, p . Using a nonlinear least squares fit algorithm and the physical assumption that the one-sided Lower Tolerance Limit ( LTL ), at 95% confidence level, of the fatigue life, i.e., the minimum cycles-to-failure, minNf , of a full-scale component, cannot be negative as the lack or "Failure" of coverage ( Fp ), defined as 1 - p , approaches zero, we develop a new fatigue life model, where the minimum cycles-to-failure, minNf , at extremely low "Failure" of coverage, Fp , can be estimated. Since the concept of coverage is closely related to that of an inspection strategy, and if one assumes that the predominent cause of failure of a full-size component is due to the "Failure" of inspection or coverage, it is reasonable to equate the quantity, Fp , to a Failure Probability, FP , thereby leading to a new approach of estimating the frequency of in-service inspection of a full-size component. To illustrate this approach, we include a numerical example using the published data of the fatigue of an AISI 4340 steel (N.E. Dowling, Journal of Testing and Evaluation , ASTM, Vol. 1(4) (1973), 271-287) and a linear least squares fit to generate the necessary uncertainties for performing a dynamic risk analysis, where a graphical plot of an estimate of risk with uncertainty vs. a predicted most likely date of a high consequence failure event becomes available. In addition, a nonlinear least squares logistic function fit of the fatigue data yields a prediction of the statistical distribution of both the ultimate strength and the endurance limit.

Uncertainty in multi-scale fatigue life modeling and a new approach to estimating frequency of in-service inspection of aging components