Modeling and Analysis of Dependable Systems

The following sections are included:

• Dedication
• Preface
• Contents
• Acronym List

The following sections are included:

• System Dependability: Basic Notions
  • Dependability evaluation
  • Measures of dependability
  • The probabilistic approach
• Combinatorial Models
  • Fault Tree
  • Dynamic Fault Tree
• State Space Models
  • Markov Chains
  • Petri Nets

As we have discussed in the previous chapter, the typical approach to dependability and reliability analysis is the probabilistic one. This means that a probabilistic model of the system to be analyzed has to be constructed…

As we have discussed in Chapter 1, Fault Tree Analysis (FTA) is a very popular and diffused technique for the dependability modeling and evaluation of large, safety-critical systems [Henley and Kumamoto (1981); Leveson (1995)]…

In Chapter 3, we showed that the modeling possibilities offered by FT, can be extended by relying on BN. This allows us to relax some constraints which are typical of FT. It has been shown how FT can be directly mapped into BN, and that the basic inference techniques on the latter may be used to obtain classical parameters computed from the former. In addition, BN allow to represent local dependencies and to perform both predictive and diagnostic reasoning. In this chapter, we show how Dynamic Bayesian Networks (DBN) can provide a unified framework in which Dynamic Fault Trees (DFT) can be represented. As we have introduced in Chapter 1 (Section 1.2.2), DFT introduce four types of dynamic gates: WSP, FDEP, PAND and SEQ. WSP represents situations where spare components are available, and special cases are the CSP gate (when spares cannot fail while in stand-by mode) and the HSP gate (when spares have the same failure rate both in stand-by and in operative mode). We have also noticed that SEQ gates can be modeled as a special case of a CSP (Section 1.2.2) [Montani et al. (2005)], so we do not consider such gates in the following. Furthermore, the FDEP gate can be generalized to the Probabilistic Dependency gate (PDEP) [Portinale et al. (2010)] where the trigger event T causes other dependent components to become unusable or inaccessible with a probability π_d ≤1. In particular, if π_d = 1 we obtain the standard FDEP (i.e., dependent components are forced to definitely fail when the trigger occurs), while if π_d < 1 we can model different failure dependencies (we will discuss these aspects in more detail in the following)…

In the previous chapters, we have seen that Probabilistic Graphical Models like Bayesian Networks or Dynamic Bayesian Networks are very useful to study dependability properties of systems, such as component and system reliability, fault prediction and fault diagnosis. Concerning the maintainability aspect, while it is possible to introduce the concept of repair policy (see Chapter 4), this is limited to the possibility of modeling a stochastic repair process, with the assumption that, once a given component fails, then, with some stochastic delay, it will be eventually repaired or replaced with a working component. This is in line with the notion of maintainability as introduced in Chapter 1; however, this framework does not address the issue of preventive maintenance, and it does not deal with the problem of selecting the “best” maintenance actions or procedures…

In this chapter, we describe a software tool which allows one to analyze a DFT relying on its conversion into a DBN. The tool is called RADy-BaN [Portinale et al. (2007, 2010); Montani et al. (2008)] which means Reliability Analysis with Dynamic Bayesian Networks; it implements the modular algorithm described in Chapter 4 for automatically translating a DFT into the corresponding DBN; it then exploits standard algorithms for the inference on DBN, in order to compute reliability measures, and in particular the 1.5JT and BK inference algorithms (see Chapter 2)…

The following sections are included:

• Problem Introduction
• Modeling Cascading Failures by Means of DBN
  • Building the DBN model
  • The cascading failure scenario
• Quantitative Results

The following sections are included:

• Problem Introduction
• The Testing Environment
• Off-board Process
  • DFT model of the case study
  • DBN model of the case study
• On-board Process
• Testing ARPHA

The following sections are included:

• Problem Introduction
• Attack Tree Based Formalisms
• Decision Networks for Attack/Defense Scenarios
  • From Attack Countermeasure Trees to Decision Networks
  • Quantitative analysis

The following sections are included:

• Problem Introduction
• The Benchmark
  • Version 1: basic system
  • Version 2: state dependent failure rates
  • Version 3: controller failure on demand
  • Version 4: repairable components
• Related Work
• DBN Models of the Benchmark
  • Modelling Version 1
  • Modelling Versions 2 and 3
  • Modelling Version 4
• DBN Analysis Results
  • Predictive analysis
  • Diagnostic analysis

The following sections is included:

• JT Algorithm for Static Bayesian Networks
  • Constructing the Junction/Join Tree
  • Belief Propagation on Junction Tree
• JT Algorithm for Dynamic Bayesian Networks
  • The 1.5JT algorithm
  • The Boyen-Koller algorithm

The following sections are included:

• Bibliography
• Index