The external load factor (χ) is a key parameter affecting the performance and reliability of bolted joints. This study presents an integrated framework combining experimental measurement, physics-informed surrogate modeling, and reliability-based robust design optimization (RBRDO) to analyze and optimize χ under uncertainty. A structured experimental design is employed to investigate the effects of friction coefficient (μ), surface roughness (Ra), and material hardness (HB). Results indicate significant nonlinear interactions, with material hardness exerting the strongest influence. A physics-informed surrogate model is then developed to provide accurate and physically consistent predictions. The optimization framework incorporates the expected value, variance, and Conditional Value-at-Risk (CVaR) to balance performance, variability, and risk. The optimal design, characterized by higher friction, lower surface roughness, and greater material hardness, reduces the expected external load factor to approximately 0.24 while satisfying the reliability requirement P(0.2 < χ < 0.3) ≈ 0.9993. The proposed framework offers an efficient and robust methodology for mechanical design under uncertainty.