In the case of ASME Class 1 pressure vessels and piping code, as in other similar codes, the design adequacy for fatigue is based on the cumulative usage factor (CUF), with recent augmentation to account for possible environmental effects. This deterministic quantification utilizes several engineering parameters (inputs) and (multiplicative) empirical factors. Although the fixed values of some of these design factors and S–N curves are based on underlying experimental data, the associated uncertainties are not explicit in the resulting fatigue assessment that is effectively based on the singular, calculated quantities of CUF and Fen, projected for a specified service. As such, the resulting fatigue margin and associated conservatism remain implicit or inconsistent and unquantifiable.

At the same time, there is an increased demand for either extending the life of existing systems or for new systems with economically viable or better optimized fatigue designs. One approach to address this is to use a more realistic evaluation offered by probabilistic techniques that take into account the various uncertainties. Such an approach to supplement the deterministic analysis was recently proposed by the author keeping the existing and familiar framework of CUF based assessment, while satisfying acceptable component reliability to meet the fatigue design adequacy. The CUF formulation includes an explicit consideration of the k-factors (for material, loading history, surface and size effects) as adjustments to the S–N data. The objective of this paper is to assess the impact of k-factors and their uncertainty on the failure probability and on the number of load-cycles for specified target reliability. Also, similar assessment is made for the impact of strain-rate variable and its uncertainty on the allowable load-cycles. This is illustrated with a typical application of the CUF analysis of a safety injection nozzle safe-end. The approach taken consists of parametric analysis of the CUF-based probability of failure by individually removing the factors and/or their uncertainty, and comparing the results with the base case where all factors and associated uncertainties are maintained at their original values. Results of this analysis and their implications are discussed, along with a generally applicable relation between the deterministic CUF and the probability of failure.

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