Fitting fatigue data with a bi-conditional model

The formulation of a probability-stress-life (P-S-N) curve is a necessary step beyond the basic S-N relation when dealing with reliability. This paper presents a model, relevant to materials that exhibits a fatigue limit, which considers the number of cycles to failure and the occurrence of the failure itself as statistically independent events, described with different distributions and/or different degree of scatter. Combining these two as a parallel system leads to the proposed model. In the case where the S-N relation is a Basquin's law, the formulations of the probability density function, cumulative distribution function, quantiles, parameter and quantile confidence interval are presented in a procedure that allows practically any testing strategy. The result is a flexible model combined with the tools that deliver a wide range of information needed in the design phase. Finally, an extension to include static strength and applicability to fatigue crack growth and defects-based fatigue approach are presented.