The primary sources of multi-parameter identification bias in six degree-of-freedom (DOF) robotic manipulators are the highly coupled model parameters and complex linkage relationships. Such intricate multi-parameter identification chains make it challenging to conduct accurate error assessment, thereby affecting the compensation of the manipulator′s operational accuracy. To address this challenge, a grey-correlation-analysis-based error analysis method for parametric calibration models is proposed, which reveals the error propagation relationships within highly coupled multi-parameter identification chains. First, based on the analysis of error propagation chains for identified parameters, a robotic manipulator calibration error model is established to achieve the quantitative decomposition of Cartesian pose errors in joint space. Second, through the synergistic integration of parameter identification algorithms and error propagation chains, the error values of joint parameter sequences are estimated. To address the strong coupling characteristics of parameter deviations, the grey relational analysis method is introduced. By calculating the correlation coefficients between various parameters, the interrelationships among the characteristic parameters of each joint axis are quantitatively evaluated, thereby determining the priority of error compensation. Experimental results indicate that, compared to translational errors, rotational errors exhibit stronger coupling characteristics during their propagation through the kinematic chain. Through comparative analysis of positioning and orientation errors, it was found that the angular deviations in the first three joints, particularly those along the y-axis direction, contribute most significantly to the end-effector′s overall error. Therefore, these critical parameters should be prioritized in error compensation. Experimental data show that the final positioning error is 3.90 mm, with an orientation error of 0.06°. This study improves the calibration efficiency of robotic arms by decoupling complex parameter linkages, quantifying error contributions, and integrating sensitivity analysis of error parameters to develop an optimized compensation strategy.