We present an efficient method for evaluating random phase errors in phase shifters within photonic integrated circuits, avoiding the computational cost of traditional Monte Carlo simulations. By modeling spatially correlated manufacturing variations as a stationary Gaussian process and applying linear functional theory, our approach enables rapid prediction of phase difference distributions through numerical integration. We validate the method using tolerance optimization and virtual manufacturing experiments, demonstrating its accuracy and significant reduction in computational burden. This framework offers a practical and scalable alternative for error analysis and robust design in photonic systems.