Luigi Portinale

Improving the analysis of dependable systems by mapping fault trees into Bayesian networks

Abstract Bayesian Networks (BN) provide a robust probabilistic method of reasoning under uncertainty. They have been successfully applied in a variety of real-world tasks but they have received little attention in the area of dependability. The present paper is aimed at exploring the capabilities of the BN formalism in the analysis of dependable systems. To this end, the paper compares BN with one of the most popular techniques for dependability analysis of large, safety critical systems, namely Fault Trees (FT). The paper shows that any FT can be directly mapped into a BN and that basic inference techniques on the latter may be used to obtain classical parameters computed from the former (i.e. reliability of the Top Event or of any sub-system, criticality of components, etc). Moreover, by using BN, some additional power can be obtained, both at the modeling and at the analysis level. At the modeling level, several restrictive assumptions implicit in the FT methodology can be removed and various kinds of dependencies among components can be accommodated. At the analysis level, a general diagnostic analysis can be performed. The comparison of the two methodologies is carried out by means of a running example, taken from the literature, that consists of a redundant multiprocessor system.

Bayesian networks in reliability

Over the last decade, Bayesian networks (BNs) have become a popular tool for modelling many kinds of statistical problems. We have also seen a growing interest for using BNs in the reliability analysis community. In this paper we will discuss the properties of the modelling framework that make BNs particularly well suited for reliability applications, and point to ongoing research that is relevant for practitioners in reliability.

RADYBAN : A tool for reliability analysis of dynamic fault trees through conversion into dynamic Bayesian networks

In this paper, we present Radyban (Reliability Analysis with DYnamic BAyesian Networks), a software tool which allows to analyze a dynamic fault tree relying on its conversion into a dynamic Bayesian network. The tool implements a modular algorithm for automatically translating a dynamic fault tree into the corresponding dynamic Bayesian network and exploits classical algorithms for the inference on dynamic Bayesian networks, in order to compute reliability measures. After having described the basic features of the tool, we show how it operates on a real world example and we compare the unreliability results it generates with those returned by other methodologies, in order to verify the correctness and the consistency of the results obtained.

Parametric fault tree for the dependability analysis of redundant systems and its high-level Petri net semantics

In order to cope efficiently with the dependability analysis of redundant systems with replicated units, a new, more compact fault-tree formalism, called Parametric Fault Tree (PFT), is defined. In a PFT formalism, replicated units are folded and indexed so that only one representative of the similar replicas is included in the model. From the PFT, a list of parametric cut sets can be derived, where only the relevant patterns leading to the system failure are evidenced regardless of the actual identity of the component in the cut set. The paper provides an algorithm to convert a PFT into a class of High-Level Petri Nets, called SWN. The purpose of this conversion is twofold: to exploit the modeling power and flexibility of the SWN formalism, allowing the analyst to include statistical dependencies that could not have been accommodated into the corresponding PFT and to exploit the capability of the SWN formalism to generate a lumped Markov chain, thus alleviating the state explosion problem. The search for the minimal cut sets (qualitative analysis) can be often performed by a structural T-invariant analysis on the generated SWN. The advantages that can be obtained from the translation of a PFT into a SWN are investigated considering a fault-tolerant multiprocessor system example.

Supporting reliability engineers in exploiting the power of Dynamic Bayesian Networks

In this paper, we present an approach to reliability modeling and analysis based on the automatic conversion of a particular reliability engineering model, the Dynamic Fault Tree (DFT), into Dynamic Bayesian Networks (DBN). The approach is implemented in a software tool called RADYBAN (Reliability Analysis with DYnamic BAyesian Networks). The aim is to provide a familiar interface to reliability engineers, by allowing them to model the system to be analyzed with a standard formalism; however, a modular algorithm is implemented to automatically compile a DFT into the corresponding DBN. In fact, when the computation of specific reliability measures is requested, classical algorithms for the inference on Dynamic Bayesian Networks are exploited, in order to compute the requested parameters. This is performed in a totally transparent way to the user, who could in principle be completely unaware of the underlying Bayesian Network. The use of DBNs allows the user to be able to compute measures that are not directly computable from DFTs, but that are naturally obtainable from DBN inference. Moreover, the modeling capabilities of a DBN, allow us to extend the basic DFT formalism, by introducing probabilistic dependencies among system components, as well as the definition of specific repair policies that can be taken into account during the reliability analysis phase. We finally show how the approach operates on some specific examples, by describing the advantages of having available a full inference engine based on DBNs for the requested analysis tasks.

Multi-modal diagnosis combining case-based and model-based reasoning: a formal and experimental analysis

Integrating different reasoning modes in the construction of an intelligent system is one of the most interesting and challenging aspects of modern AI. Exploiting the complementarity and the synergy of different approaches is one of the main motivations that led several researchers to investigate the possibilities of building multi-modal reasoning systems, where different reasoning modalities and different knowledge representation formalisms are integrated and combined. Case-Based Reasoning (CBR) is often considered a fundamental modality in several multi-modal reasoning systems; CBR integration has been shown very useful and practical in several domains and tasks. The right way of devising a CBR integration is however very complex and a principled way of combining different modalities is needed to gain the maximum effectiveness and efficiency for a particular task. In this paper we present results (both theoretical and experimental) concerning architectures integrating CBR and Model-Based Reasoning (MBR) in the context of diagnostic problem solving. We first show that both the MBR and CBR approaches to diagnosis may suffer from computational intractability, and therefore a careful combination of the two approaches may be useful to reduce the computational cost in the average case. The most important contribution of the paper is the analysis of the different facets that may influence the entire performance of a multi-modal reasoning system, namely computational complexity, system competence in problem solving and the quality of the sets of produced solutions. We show that an opportunistic and flexible architecture able to estimate the right cooperation among modalities can exhibit a satisfactory behavior with respect to every performance aspect. An analysis of different ways of integrating CBR is performed both at the experimental and at the analytical level. On the analytical side, a cost model and a competence model able to analyze a multi-modal architecture through the analysis of its individual components are introduced and discussed. On the experimental side, a very detailed set of experiments has been carried out, showing that a flexible and opportunistic integration can provide significant advantages in the use of a multi-modal architecture.

Retrieval in a Prototype-Based Case Library: A Case Study in Diabetes Therapy Revision

Case retrieval is a complex and important stage of the overall CBR process, involving situation assessment and a flexible combination of case memory search and matching. The goal of the paper is to discuss a retrieval approach in a case library organized through classes of prototypes. Situation assessment is realized with a Bayesian classification step, aimed at defining a uniform framework for feature evaluation and at restricting search only to relevant parts of the case library. Classical K-NN methods or pruning based technique like Pivoting-Based Retrieval can then be applied to retrieve and match cases, by considering intra-class or inter-class retrieval. The proposed method has been evaluated within a decision support system for the therapy revision of patients affected by Diabetes Mellitus.

ADAPtER: An Integrated Diagnostic System Combining Case-Based and Abductive Reasoning

The aim of this paper is to describe the ADAPtER system, a diagnostic architecture combining case-based reasoning with abductive reasoning and exploiting the adaptation of the solution of old episodes, in order to focus the reasoning process. Domain knowledge is represented via a logical model and basic mechanisms, based on abductive reasoning with consistency constraints, have been defined for solving complex diagnostic problems involving multiple faults. The model-based component has been supplemented with a case memory and adaptation mechanisms have been developed, in order to make the diagnostic system able to exploit past experience in solving new cases. A heuristic function is proposed, able to rank the solutions associated to retrieved cases with respect to the adaptation effort needed to transform such solutions into possible solutions for the current case. We will discuss some preliminary experiments showing the validity of the above heuristic and the convenience of solving a new case by adapting a retrieved solution rather than solving the new problem from scratch.

ACCOUNTING FOR THE TEMPORAL DIMENSION IN CASE-BASED RETRIEVAL: A FRAMEWORK FOR MEDICAL APPLICATIONS

Time‐varying information embedded in cases has often been neglected and its role oversimplified in case‐based reasoning systems. In several real‐world problems, and in particular in medical applications, a case should capture the evolution of the observed phenomenon over time. To this end, we propose to represent temporal information at two levels: (1) at the case level, when some features are collected in the form of time series, because they describe parameters varying within a period of time (which corresponds to the case duration), and we aim at analyzing the system behavior within the case duration interval itself; (2) at the history level, when we are interested in reconstructing the evolution of the system by retrieving temporally related cases. In this paper, we describe a framework for case representation and retrieval that is able to take into account the temporal dimension, and is meant to be used in any time dependent domain, which is particularly well suited for medical applications. To support case retrieval, we provide an analysis of similarity‐based time series retrieval techniques; to support history retrieval, we introduce possible ways to summarize the case content, together with the corresponding strategies for identifying similar instances in the knowledge base. A concrete application of our framework is represented by Rhene, a system for intelligent retrieval in the hemodialysis domain.

Comparing Fault Trees and Bayesian Networks for Dependability Analysis

Bayesian Networks (BN) provide a robust probabilistic method of reasoning under uncertainty. They have been successfully applied in a variety of real-world tasks and their suitability for dependability analysis is now considered by several researchers. In the present paper, we aim at defining a formal comparison between BN and one of the most popular techniques for dependability analysis: Fault Trees (FT). We will show that any FT can be easily mapped into a BN and that basic inference techniques on the latter may be used to obtain classical parameters computed using the former (i.e. reliability of the Top Event or of any sub-system, criticality of components, etc...). Moreover, we will discuss how, by using BN, some additional power can be obtained, both at the modeling and at the analysis level. In particular, dependency among components and noisy gates can be easily accommodated in the BN framework, together with the possibility of performing general diagnostic analysis. The comparison of the two methodologies is carried on through the analysis of an example that consists of a redundant multiprocessor system, with local and shared memories, local mirrored disks and a single bus.