Statistical Analysis and Probabilistic Characterization of the Mechanical Behavior of ABS: Application of Student’s t-Distribution and Weibull Distribution

¹ Hassan II University of Casablanca (UH2C), National Higher School of Electricity and Mechanics, Laboratory of Mechanics, Engineering and Innovation, Km 8 Route d’El Jadida, B.P 5366 Maarif Casablanca 20100 Morocco.
² Higher Institute of Maritimes Studies, Casablanca Morocco
³ Higher Institute of Marine Fisheries-Agadir, Morocco
⁴ Laboratory of energy Engineering, Materials and Systems, ENSA, Ibn Zoher University, Agadir

Abstract

This study, presents a detailed of a statistical study of how acrylonitrile butadiene styrene (ABS) behaves mechanically when subjected to uniaxial tensile testing. By combining Student’s t-distribution with the Weibull distribution, we capture the variability in mechanical properties and build robust reliability models. Our analysis covers both flawless specimens and those containing geometric flaws, such as notches and holes. From the data, we identified crucial statistical parameters, established 90% confidence intervals, and set design guidelines to ensure a 99% probability of survival. Importantly, the study highlights how these geometric defects significantly weaken the material’s load capacity. This probabilistic framework equips engineers with valuable insights to optimize ABS component design and reliably predict their performance in real-world applications.