Integrated avionics system is an important feature of the new generation of aircraft, and its reliability and stability play a decisive role in the flight and safety of the entire aircraft. As the avionics system should possess high reliability, a distributed cluster redundancy architecture is proposed, and the corresponding redundancy management scheme is designed to tolerate Byzantine errors that may occur after avionics system failure and effectively improve the reliability and fault tolerance of fault-tolerant computers. The proposed redundancy management scheme is optimized by the two schemes of threshold signature and cluster selection to reduce the communication overhead between redundancy computers in the cluster, avoid affecting the real-time performance of the avionics system, and improve the redundancy management efficiency. Through simulation experiments, the results verify that the distributed cluster redundancy management scheme can effectively improve the reliability of the avionics system and enhance Byzantine resilience. Meanwhile, in an n-redundancy avionics system, the system can still operate correctly as long as the number of Byzantine nodes is less than n/3, and the optimization scheme has lower communication and computing costs.