<p>Since its inception, the Shields curve has been a fundamental tool for analyzing sediment entrainment thresholds. Nevertheless, the original formulation contains inherent limitations: both sides of its governing equation incorporate interdependent hydrodynamic parameters (flow velocity and shear stress), rendering explicit determination of the critical incipient shear stress mathematically intractable. To address this circular dependency, researchers have developed revised methodologies involving auxiliary dimensionless parameters and direct computational frameworks. This study synthesizes the prevalent Shields curve variants and their associated dimensionless parameters, and systematically evaluates their predictive accuracy using experimental data from flume tests documented in the literature. Sensitivity analyses of Shields parameters reveal that while different dimensionless parameters exhibit distinct functional forms, they maintain strong mutual correlations. When constrained by identical shear stress solution parameters, formulations combining any pair of dimensionless parameters achieve comparable computational precision. Correlation analyses further demonstrate that parameterization schemes incorporating the particle Reynolds number minimize experimental data scatter. Through regression modeling, a novel expression for critical shear stress of non-cohesive particles is proposed. Comparative validation confirms that the new model outperforms the conventional approaches in both predictive accuracy and experimental agreement.</p>