Modeling Fatigue Data of Complex Metallic Alloys Using a Generalized Student’s t-Birnbaum–Saunders Family of Lifetime Models: A Comparative Study with Applications

The mechanical reliability of metallic alloys under cyclic loading is crucial for optimizing their microstructure–property relationships. Understanding the statistical behavior of fatigue failure data is essential for designing alloys that endure extreme environmental conditions. This study introduces a generalization of the Student’s t-Birnbaum–Saunders distribution to improve the modeling of fatigue life data, which often exhibit heavy tails and are common in advanced alloy systems. Seven different estimation methods are employed to estimate and compare the parameters of the proposed distribution, providing a comprehensive statistical framework for fatigue failure analysis. The goodness-of-fit of the proposed model and its sub-models, along with the joint relative efficiency of parameter estimates, is assessed using real fatigue data within the maximum likelihood framework. Additionally, the robustness of estimation methods is examined through Monte Carlo simulations across various sample sizes and parameter configurations. The results highlight the effectiveness of the generalized Student’s t-Birnbaum–Saunders distribution in capturing the stochastic nature of fatigue failure in metallic alloys, offering valuable insights for materials design and predictive reliability modeling. These findings align with advancements in computational modeling and simulation, contributing to developing alloys with tailored mechanical properties.