Algorithms for Bayesian network modeling and reliability inference of complex multistate systems: Part I - Independent systems

As the number of complex multistate systems' components increases, one major challenge to analyze the reliabilities of complex multistate systems by Bayesian network (BN) is that the memory storage requirements (MSRs) of conditional probability table (CPT) increase exponentially. When the components reach a certain amount, the MSRs of CPT will exceed the computer's random access memory (RAM). To solve this problem, this two-part paper proposes a novel multistate compression algorithm to compress the CPT so that the MSRs of CPT can be reduced apparently. In this Part I, an independent multistate inference algorithm is proposed to perform the inference of BN based on the compressed CPT for the complex multistate independent systems. Given the evidence of system, the backward inference algorithm is proposed to update the probability distributions of compoents. The above proposed algorithms can be generally applied to any complex multistate independent system without constraints on system structure and state configurations. In addition, the Part II studies the application of compression idea in the complex multistate dependent systems. Finally, two case studies are used to validate the performance of the proposed algorithms.