Reliability and Failure Probability Analysis of Al-Mg-Si/Al2O3–SiC Composites Cast Under Different Mold Conditions Using Classical and Bayesian Weibull Models

This study analyzes the compressive behavior and reliability of Al-Mg-Si (6061) metal matrix composites reinforced with different weight fractions of Al2O3 and SiC ceramics and cast with graphite and steel molds. Compression tests were carried out according to ASTM E9 with 0–8 wt.% reinforcement. The mold material significantly influenced the strength due to the cooling rate and interfacial adhesion. A two-parameter Weibull model assessed statistical reliability and extracted the shape (β) and scale (η) parameters using linear regression. Advanced models—lifelines (frequentist) and Bayesian models—were also applied. Graphite molds yielded composites with higher shape parameters (β = 6.27 for Al2O3; 5.49 for SiC) than steel molds (β = 4.66 for Al2O3; 4.79 for SiC). The scale values ranged from 490–523 MPa. The lifelines showed similar trends, with the graphite molds exhibiting higher consistency and scale (ρ = 7.45–9.36, λ = 479.71–517.49 MPa). Bayesian modeling using PyMC provided posterior distributions that better captured the uncertainty. Graphite mold samples had higher shape parameters (α = 6.98 for Al2O3; 8.46 for SiC) and scale values of 489.07–530.64 MPa. Bayesian models provided wider reliability limits, especially for SiC steel. Both methods confirmed the Weibull behavior. Lifelines proved to be computationally efficient, while Bayesian analysis provided deeper insight into reliability and variability.