Reliability allocation of the system with k-out-of-n: G subsystems considering K-mixed redundancy strategy and heterogeneous components

Redundancy has been widely adopted in complex engineering systems as a critical reliability enhancement approach. For a system with k-out-of-n: G subsystems(k≥1) under a K-mixed redundancy strategy with heterogeneous components following arbitrary failure distributions, current research has provided limited comprehensive methods for solving the redundancy allocation problem (RAP). In this paper, an RAP-solving method based on dynamic fault trees and conditional binary decision diagrams (DFT-CBDD) is proposed for system modeling. By introducing a conditional event, the dynamic fault tree (DFT) model is transformed into the conditional binary decision diagram (CBDD) structure to identify minimum cut sets (MCSs). The exact analytical formulation of system reliability was derived from the failure logic of the MCSs. Then, a novel mathematical model was developed for the redundancy optimization of series-parallel systems with k-out-of-n: G subsystems, solved using the designed genetic algorithm (GA). The proposed method is verified to obtain exact reliability in a shorter time by comparing subsystem evaluations with classical methods, and its effectiveness and robustness are demonstrated by solving the RAP of a practical series-parallel system under different constraints and redundancy strategies.