The belief noisy-or model applied to network reliability analysis
This work addresses the knowledge engineering bottleneck in Bayesian Networks for engineers, offering a more flexible modeling approach, though it is incremental as it builds on the existing Noisy-OR gate.
The paper tackles the exponential parameter growth in Bayesian Network CPTs by proposing the Belief Noisy-OR (BNOR) model, an extension of the Noisy-OR gate that handles both aleatory and epistemic uncertainty, and demonstrates its effectiveness in network reliability analysis.
One difficulty faced in knowledge engineering for Bayesian Network (BN) is the quan-tification step where the Conditional Probability Tables (CPTs) are determined. The number of parameters included in CPTs increases exponentially with the number of parent variables. The most common solution is the application of the so-called canonical gates. The Noisy-OR (NOR) gate, which takes advantage of the independence of causal interactions, provides a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, an extension of NOR model based on the theory of belief functions, named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both aleatory and epistemic uncertainty of the network. Compared with NOR, more rich information which is of great value for making decisions can be got when the available knowledge is uncertain. Specially, when there is no epistemic uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR are presented in this paper in order to meet various needs of engineers. The application of BNOR model on the reliability evaluation problem of networked systems demonstrates its effectiveness.