Temporal noisy-adder of bayesian network for scalable consecutive-k-out-of-n:F system reliability analysis

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The Bayesian network(BN) is a powerful tool for modeling and analyzing reliability, safety, and risk in various engineering systems. Although there have been studies that incorporate it into the modeling of Consecutive-k-out-of-n: F systems(C(k,n:F)), these applications are limited to naive mode and cannot tackle scalable systems (e.g., n>2000,k>40). By introducing temporal Noisy-adder structure, named NaCkoon model, the number of nodes in equivalent C(k,n:F) BN model is significantly reduced, and the Conditional Probability Table (CPT) of temporary nodes can be controlled to linear complexity. The correctness of the proposed algorithm is validated by the comparison of literature case. Through numerical experiments, the novel algorithms proposed in this paper were compared with existing ones, including BN construction and inference computation time, was found to be the most optimal solution. Finally, the computable ranges of novel and existing algorithms are obtained through the capability computation. The test results show that NaCkoon model proposed in this paper has great advantages over existing algorithms and proposed NaA+NaO model based BN.