In the civil aviation system, the Inertial Measurement Unit (IMU)/ Global Navigation Satellite System (GNSS) integrated navigation remains the most effective navigation scheme. Based upon this, the utilization of redundant IMUs and a multi-constellation system can significantly enhance navigation and integrity performance. However, a redundant IMUs/GNSS integrated navigation system is susceptible to more complex failure modes, including GNSS faults (satellite and constellation faults) and IMU fault. Additionally, dealing with correlated measurements between redundant construction presents a challenging issue. Therefore, we propose an integrity monitoring method for decentralized redundant IMUs/GNSS integrated navigation system. This method considers GNSS faults and IMU fault in the integrity monitoring process, specifically designed for decentralized filter construction with redundancy. Furthermore, due to the correlated measurements between redundant filters, optimal fusion coefficients are determined by considering the unbiased estimate and minimizing the trace of covariance of primary filter. An optimal allocation scheme of continuity risk is also established to improve navigation and integrity performance. Simulation results demonstrate the feasibility and effectiveness of the proposed integrity monitoring method. Moreover, in the context of correlated measurements, the integrated navigation system also exhibits superiority.