Abstract: To address the reduced accuracy in reliability analysis of composite structures due to parameter correlations, this study proposes a Copula-Kriging Synergistic Reliability Method (CK-SRM). By integrating joint probability modeling and surrogate model optimization, CK-SRM quantifies the statistical dependencies of elastic parameters, overcoming the limitations of traditional independent assumptions. The model is validated via buckling tests and engineering computational methods. A Kriging surrogate model is constructed using Latin Hypercube Sampling and parametric finite element modeling to predict buckling loads. A quantitative mapping relationship among parameter correlations, reliability, and load-bearing capacity is established. Gaussian copula-based sampling is employed to analyze reliability and structural capacity under Single Flight Probability of Failure of 10⁻⁷. Sensitivity analysis evaluates the impacts of parameter correlations. Results demonstrate that considering parameter correlations improves the load-bearing capacity of composite stiffened panels by 4.7% compared to deterministic design based on the safety factor method. This method provides critical insights for optimizing composite stiffened panel designs, enhancing structural safety, and fully leveraging material performance.