*3.4. Uncertainty Quantification*

The procedure outlined in the previous subsection quantifies uncertainty in fatigue damage accumulation. However, the probabilistic model (1) requires uncertainty in stress ranges rather than in the fatigue damage. Therefore, it is now described how uncertainty in fatigue damage can be transformed into uncertainty in stress ranges, as indicated in step four in Figure 2.

The fatigue damage accumulation, *D*, is proportional to the stress ranges, Δ*s*, according to *D* ∝ Δ*s<sup>m</sup>* (assuming a linear SN curve), from which it follows Δ*s* ∝ *D*1/*m*. The stress range distribution parameters can be computed from Monte Carlo simulations. Alternatively, assuming the damage distribution function is normal, the stress range distribution's mean, *μ*Δ*s*, and coefficient of variation (CoV), *c*Δ*s*, can be approximated as

$$
\mu\_{\Lambda s} = \mu\_i^{1/m} \tag{5}
$$

and

$$
\omega\_{\Lambda s} = \frac{c\_i}{m'} \tag{6}
$$

where *μ<sup>i</sup>* and *ci* are the mean and CoV of the fatigue damage distribution due to the uncertainty associated with *αj*.
