Optimization Method for Reliability–Redundancy Allocation Problem in Large Hybrid Binary Systems

This paper addresses a well-known research topic in the design of complex systems, specifically within the class of reliability optimization problems (ROPs). It focuses on optimal reliability–redundancy allocation problems (RRAPs) for large binary systems with hybrid structures. Two main objectives are considered: (1) to maximize system reliability under cost and volume constraints, and (2) to achieve the required reliability at minimal cost under a volume constraint. The system reliability model includes components with only two states: normal operating or failed. High reliability can result from directly improving component reliability, allocating redundancy, or using both approaches together. Several redundancy strategies are covered: active, passive, hybrid standby with hot, warm, or cold spares, static redundancy such as TMR and 5MR, TMR structures with control logic and spares, and reconfigurable TMR/Simplex structures. The proposed method uses a zero–one integer programming formulation that applies log-transformed reliability functions and binary decision variables to represent subsystem configurations. The experimental results validate the approach and confirm its efficiency.