Benefits of Bayesian Network Models

3Bayesian Network: Modeling Formalism of the Structure Function of Multi-State Systems

3.1. Introduction

In the case of multi-state systems, standard dependability methods, proposed in the literature are difficult to implement [LIS 03]. In this section, the methodology previously presented in the Boolean case is transposed to multi-state systems to prove that it is easy to obtain multi-state models with BN. Methods are presented for the construction of a model of multi-state systems. The methods are based on cut-sets, tie-sets or the principle of top-down analysis based on functional analysis. Section 3.2.3 explains the functional analysis-based method and explains how it provides an easy way to build an efficient model.

3.2. BN models in the multi-state case

The first step when modeling a multi-state model for dependability analysis is to define the set of variables x_i that represent the component states [SHU 10] as follows:

[3.1]

with l_i being the first failure state, i.e. the component does not satisfy its functioning goals. States 1 … (l_i – 1) are degraded functioning states, i.e. the component is not fully functional but it does not compromise the system mission. States l_i … n_i are several failure states of the component that can have different consequences on the system state.

The system state is also defined by a multi-state variable with respect to different functioning ...