A novel reliability redundancy allocation problem formulation for complex systems

Reliability Redundancy Allocation Problem (RRAP) aims to optimize system design with respect to certain resource constraints. For the most of RRAP studies, it is commonly assumed that the subsystems form a series-parallel or bridge structure, while the redundant components in the same subsystem are placed in parallel. To generalize system structures, this paper proposes a novel RRAP for complex systems. The complex system structure is modeled with a graph, where the vertices and edges represent the components and connections between them, respectively. To calculate the system reliability from its structure graph, an automated calculation method based on functionality multi-graph is put forward. The components are classified into various clusters based on the system functionalities they provide, then a multi-graph is constructed by fusing the vertices in the same cluster into a hyper-vertex. Spanning trees are derived from functionality multi-graph, and a validity test is performed to identify valid system configurations. On this basis, a factoring theorem-based algorithm is devised to calculate system reliability. Comparative experiments are carried out on six benchmark problems, the results of which compare favorably to previous RRAP studies. A case study of security system design is also conducted to demonstrate the practicality of our proposed method.