PSI - Issue 79

Available online at www.sciencedirect.com

ScienceDirect

Procedia Structural Integrity 79 (2026) 361–369

© 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IGF28 - MedFract3 organizers Abstract The statistical evaluation of S-N curves often involves censored data in the form of runouts. While the qualitative e ff ect of runouts on parameter estimation is well understood, their influence on the width and reliability of confidence intervals has not been sys tematically quantified. This study focuses on the bilinear S-N curve model and investigates how varying proportions of runouts in the dataset influence the confidence intervals of key model parameters, including the stress and number of cycles at the knee point, as well as the slope parameters. Using maximum likelihood estimation within a probabilistic framework based on a log-normal distribution, a Monte Carlo simulation is performed in which the proportion of runouts is systematically varied. Confidence inter vals are derived using the likelihood ratio method, which is particularly suitable for an appropriate treatment of runouts. This work provides a quantitative foundation for understanding the impact of runouts on uncertainty in bilinear S-N curve models and o ff ers practical guidance for test planning and model interpretation in fatigue analysis. 28th International Conference on Fracture and Structural Integrity - 3rd Mediterranean Conference on Fracture and Structural Integrity A Coverage Study on the E ff ect of Runouts on Confidence Intervals for Bilinear S-N Curves Felix-Christian Reissner ∗ , Jo¨rg Baumgartner Fraunhofer Institute for Structural Durability and System Reliability LBF, Bartningstraße 47, 64289 Darmstadt, Germany

Keywords: S-N curve; Confidence intervals; Likelihood ratio; Maximum likelihood estimation

1. Introduction

Fatigue design relies on an accurate characterization of the relationship between cyclic load amplitude S a , i and fatigue life N i , commonly represented by S-N curves. These models serve as the foundation for predicting fatigue life, defining design limits, and ensuring structural durability. In engineering practice, S-N curves are typically derived from experimental data containing both failures and runouts, i.e., specimens that have not failed within the test dura tion. The statistical treatment of these censored observations remains a central challenge in fatigue data evaluation. Runouts contain valuable information, as they indicate that the fatigue strength of a specimen exceeds the applied stress level for a given number of cycles. Ignoring them, as done in many conventional evaluations, can lead to bi ased parameter estimates. Modern fatigue analysis therefore incorporates runouts explicitly, for example by maximum

∗ Corresponding author. E-mail address: felix-christian.reissner@lbf.fraunhofer.de (Felix-Christian Reissner).

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IGF28 - MedFract3 organizers 10.1016/j.prostr.2025.12.346