Effective Noisy-matrix of Bayesian network for scalable m-consecutive-k-out-of-n: F models with overlapping from -1 to k-1

Bayesian network is an effective tool for reliability analysis of complex systems and have been used to compute reliability of large-scale consecutive-k-out-of-n: F models(C(k,n:F)). But for m-consecutive-k-out-of-n: F system with overlapping(m-Co(k,n:F)) with more complexities: i) condition probability table (CPT) state combination explosion of a single node, ii) more complex double-layered combination logic, iii) various overlapping scenarios. Addressing these issues, an unified and concise temporal Noisy-matrix structure of Bayesian network is proposed, which i) reduces the spatial complexity of CPT from O(2n) to O(n), ii) maps the complex combinatorial logic through a three-layer parallel structure, and iii) flexibly adapts to different overlapping scenarios by adjusting a single value in CPT of k-layer easily, iv) able to deal with large-scale model scenarios (n>2000). Several sets of comparative calculation cases from existing literature verify the correctness and efficiency of the novel approach; Moreover, by another comparative experiment of three Bayesian network-based methods demonstrates the advantages of the new approach, which can calculate a large-scale model with n=2700(5-C9(10,2700:F)) within 16 s. Finally, the limit capability diagram that can be supported by the proposed approach in different m, n, k, and o situations is given, which provides a scheme for the model's state probability calculation and may exist in various large - scale engineering scenarios.