PSI - Issue 79

Felix-Christian Reissner et al. / Procedia Structural Integrity 79 (2026) 361–369

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Series Min. number of cycles Max. number of cycles Number of samples Number of runouts N min N max n n ro A 1 · 10 4 1 · 10 7 15 0 B 1 · 10 4 5 . 6 · 10 7 15 3 Table 2: Design of experiments.

3.3. Coverage study procedure

For each parameter, the following steps are performed:

1. Generate S-N data from the base model (Eq. (1)) with the parameter set in Table 1 and standard deviation σ S , log , following the DOE settings in Table 2. 2. Estimate the (constrained) likelihoods across a grid for the parameter of interest λ , maximizing over the nuisance parameters to obtain the profile likelihood. 3. Derive the CI based on Eq. (6). 4. Record whether the true parameter is within the CI (coverage).

4. Results

4.1. Coverage results for the load amplitude at the knee point S a , k

The empirical coverage for the load at the knee point S a , k is shown in Fig. 2. The empirical coverages are comparable across the investigated confidence levels, regardless of the presence of runouts. It should be noted that the presence of runouts suppresses unrealistically low values of S a , k that occasionally occur in Series A. In all cases, the empirical coverage tends to underestimate the nominal confidence level.

Fig. 2: Profile likelihoods and confidence intervals (CI) for the load amplitude at the knee point S a , k .