Multi-Objective Optimization and Reliability Assessment of Date Palm Fiber/Sheep Wool Hybrid Polyester Composites Using RSM and Weibull Analysis

This study investigates date palm fiber (DPF) and sheep wool hybrid polyester composites with fiber loadings of 0%, 10%, 20%, and 30% by weight, fabricated by compression molding, to develop a sustainable and reliable material system. Experimental data from prior work were modeled using Weibull analysis for reliability evaluation and response surface methodology (RSM) for multi-objective optimization. Weibull statistics fitted a two-parameter distribution to tensile strength and fracture toughness, extracting shape (η) and scale ($\beta$) parameters to quantify variability and failure probability. The analysis showed that 20% hybrid content achieved the highest scale values ($\beta$ = 28.85 MPa for tensile strength and $\beta$ = 15.03 $\mathrm{M}\mathrm{P}\mathrm{a}\sqrt{\mathrm{m}}$ for fracture toughness) and comparatively low scatter (η = 10.39 and 9.2, respectively), indicating superior reliability. RSM quadratic models were developed for tensile strength, fracture toughness, thermal conductivity, acoustic attenuation, and water absorption, and were combined using desirability functions. The RSM optimization was found at 18.97% fiber content with a desirability index of 0.673, predicting 25.89 MPa tensile strength, 14.23 $\mathrm{M}\mathrm{P}\mathrm{a}\sqrt{\mathrm{m}}$ fracture toughness, 0.08 W/m·K thermal conductivity, 20.49 dB acoustic attenuation, and 5.11% water absorption. Overlaying Weibull cumulative distribution functions with RSM desirability surfaces linked probabilistic reliability zones (90–95% survival) to the deterministic optimization peak. This integration establishes a unified framework for designing natural fiber composites by embedding reliability into multi-property optimization.