The belief noisy-or model applied to network reliability analysis

TL;DR

This paper introduces the Belief Noisy-OR (BNOR) model, extending the traditional NOR gate with belief functions to handle both types of uncertainty, improving network reliability analysis.

Contribution

The paper proposes BNOR, a belief function-based extension of NOR, capable of managing epistemic and aleatory uncertainties in Bayesian networks.

Findings

BNOR effectively handles both epistemic and aleatory uncertainties.

Application to networked system reliability shows improved decision support.

BNOR reduces to NOR when no epistemic uncertainty is present.

Abstract

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.