PSI - Issue 79

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

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6. Conclusion

This study systematically quantified the e ff ect of runouts on profile-likelihood confidence intervals in bilinear S-N curve models. Across all investigated parameters, the empirical coverage was consistently below the nominal level, indicating a systematic undercoverage. The bias, however, remained moderate (typically below 15%, and less than 10% for high confidence levels), suggesting that profile-likelihood intervals remain practically useful in fatigue appli cations. Runouts primarily influenced the identifiability of the knee point N k , while their e ff ect on the load amplitude at the knee point S a , k and the slope k 1 was limited. These results highlight the importance of considering censoring ef fects in fatigue test planning and provide practical guidance on the interpretation and reliability of confidence intervals in fatigue analysis. Bartlett, M.S., 1937. Properties of su ffi ciency and statistical tests. Proceedings of the royal society of london. series a-mathematical and physical sciences 160, 268–282. Basquin, O.H., 1910. The exponential law of endurance tests, in: Proceedings of American Society of Testing Materials, pp. 625–630. Mavrakakis, M.C., 2021. Probability and statistical inference. Texts in statistical science, CRC Press, Taylor Francis Group, Boca Raton. Meeker, W.Q., Escobar, L.A., Pascual, F.G., Hong, Y., Liu, P., Falk, W.M., Ananthasayanam, B., 2024. Modern statistical models and methods for estimating fatigue-life and fatigue-strength distributions from experimental data. arXiv:2212.04550 . Meeker, W.Q., Hahn, G.J., Escobar, L.A., 2017. Statistical Intervals A Guide for Practitioners and Researchers. Wiley. Pascual, Francis G.; Meeker, W.Q., 1999. Estimating fatigue curves with the random fatigue-limit model. Technometrics 41, 277–289. doi: 10. 1080/00401706.1999.10485925 . Sto¨rzel, K., Baumgartner, J., 2021. Statistical evaluation of fatigue tests using maximum likelihood. Materials Testing 63, 714–720. doi: 10.1515/ mt-2020-0116 . Wilks, S.S., 1938. The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics 9, 60–62. doi: 10.1214/aoms/1177732360 . References