Laser powder bed fusion (LPBF), a prominent metal-based additive manufacturing (AM) technique, enables the production of complex, neat-net-shape components with minimal material waste and reduced lead times. However, achieving high final product quality is challenging due to numerous process variables and intricate, nonlinear interactions introduced by LPBF’s thermal-mechanical mechanisms. This study employs a copula-based analysis using multi-physics numerical simulations to probabilistically map relationships among process and part quality variables. Dependence and tail-dependence analyses are performed to provide deeper insights into variable interactions, enabling the identification of preferred operational windows with a balanced trade-off between product quality and productivity. The developed methodology advances the understanding of uncertainty propagation in LPBF, contributing toward improved process optimization, repeatability, and reliability.