Christophe Simon

Overview on Bayesian networks applications for dependability, risk analysis and maintenance areas

In this paper, a bibliographical review over the last decade is presented on the application of Bayesian networks to dependability, risk analysis and maintenance. It is shown an increasing trend of the literature related to these domains. This trend is due to the benefits that Bayesian networks provide in contrast with other classical methods of dependability analysis such as Markov Chains, Fault Trees and Petri Nets. Some of these benefits are the capability to model complex systems, to make predictions as well as diagnostics, to compute exactly the occurrence probability of an event, to update the calculations according to evidences, to represent multi-modal variables and to help modeling user-friendly by a graphical and compact approach. This review is based on an extraction of 200 specific references in dependability, risk analysis and maintenance applications among a database with 7000 Bayesian network references. The most representatives are presented, then discussed and some perspectives of work are provided.

Evidential Networks for Reliability Analysis and Performance Evaluation of Systems With Imprecise Knowledge

This paper deals with evidential networks to manage imprecise probabilities. Evidential networks are directed acyclic graphs that handle random, and epistemic uncertainties thanks to Dempster-Shafer structures. After we recall useful bases of the Dempster-Shafer theory, and the relation with probability intervals, we explain how to handle imprecision. Evidential networks are extended with imprecise utility functions to deal with system performance evaluation problems. We explain the application of evidential networks to system reliability evaluation problems. Then, applications to multi-state performance evaluation are proposed. The last section of the paper is devoted to study case systems.

A Fuzzy Probabilistic Approach for Determining Safety Integrity Level

The process industry has always been faced with the difficult task of determining the required integrity of safeguarding systems such as safety instrumented systems (SISs). The ANSI/ISA S84.01-1996 and IEC 61508 safety standards provide guidelines for the design, installation, operation, maintenance, and test of SIS. However, in the field, there is a considerable lack of understanding of how to apply these standards to both determine and achieve the required safety integrity level (SIL) for SIS. Moreover, in certain situations, the SIL evaluation is further complicated due to the uncertainty on reliability parameters of SIS components. This paper proposes a new approach to evaluate the ldquoconfidencerdquo of the SIL determination when there is an uncertainty about failure rates of SIS components. This approach is based on the use of failure rates and fuzzy probabilities to evaluate the SIS failure probability on demand and the SIL of the SIS. Furthermore, we provide guidance on reducing the SIL uncertainty based on fuzzy probabilistic importance measures.

Bayesian Networks and Evidence Theory to Model Complex Systems Reliability

This paper deals with the use of Bayesian Networks to compute system reliability of complex systems under epistemic uncertainty. In the context of incompleteness of reliability data and inconsistencies between the reliability model and the system modeled, the evidence theory is more suitable to manage this epistemic uncertainty. We propose to adapt the Bayesian Network model of reliability in order to integrate the evidence theory and then to produce an Evidential Network. Three examples are proposed to observe the propagation mechanism of the uncertainty through the network and its influence on the system reliability.

Imprecise reliability by evidential networks

This article deals with an implementation of probist reliability problems in evidential networks to propagate imprecise probabilities expressed as fuzzy numbers. First, the problem of imprecise knowledge in reliability problems is described concerning system and data representation. Then, the basics of the evidence theory and its use in a directed acyclic graph approach are given. The imprecise probist reliability of a complex system by modelling the component failure probabilities as real, interval, or fuzzy numbers is pointed out. Two numerical studies of systems are carried out. The results are discussed and some comparisons with a Monte-Carlo simulation and a fuzzy fault tree approach are made.

Uncertainty analysis of common cause failure in safety instrumented systems

This paper analyses the problem of epistemic uncertainty in assessing the performance of safety instrumented systems (SIS) using fault trees. The imperfect knowledge concerns the common cause failure (CCF) involved in the SIS in low demand mode. The point-valued CCF factors are replaced by fuzzy numbers, allowing experts to express their uncertainty about the CCF values. This paper shows how these uncertainties propagate through the fault tree and how this induces an uncertainty to the values of the SIS failure probability on demand and to the safety integrity level of the SIS. For the sake of verification and comparison, and to show the exactness of the approach, a Monte Carlo sampling approach is proposed, where by a uniform or triangular second-order probability distribution of CCF factors is considered.

Switching Markov chains for a holistic modeling of SIS unavailability

This paper proposes a holistic approach to model the Safety Instrumented Systems (SIS). The model is based on Switching Markov Chain and integrates several parameters like Common Cause Failure, Imperfect Proof testing, partial proof testing, etc. The basic concepts of Switching Markov Chain applied to reliability analysis are introduced and a model to compute the unavailability for a case study is presented. The proposed Switching Markov Chain allows us to assess the effect of each parameter on the SIS performance. The proposed method ensures the relevance of the results.

Bayesian networks Applications on Dependability, Risk Analysis and Maintenance

In this paper, a bibliographical review is presented about the use of Bayesian networks over the last decade on dependability, risk analysis and maintenance. It is shown an increasing trend of the literature and of the application of Bayesian networks in fields related to reliability, safety and maintenance. This trend is due to the benefits that Bayesian networks provide in contrast with other classical methods of dependability analysis such as Markov Chains and Fault Trees. Some of these benefits are: to model and to analyze complex systems, to make predictions as well as diagnostics, to compute exactly the occurrence probability of an event, to update the calculations according to evidences and to represent multimodal variables. This review is based on an extraction of 200 references; the most representative are presented.

Estimation of depth on thick edges from sharp and blurred images

This article deals with the generalization of a local depth estimation method using sharp edges and blurred edges. This Depth from Defocus method is explained and the theoretical relations are defined. Improvements concerning the generalization and the noise sensitivity on the depth estimation are developed and application conditions are exposed. Some results on synthetic images are presented to illustrate the method efficiency.

Dynamic evidential networks in system reliability analysis: A Dempster Shafer approach

Nowadays, complex manufacturing processes have to be dynamically modeled to estimate their reliability. Moreover the results computed with classical methods need to be reinforced by managing the uncertainty. To address these difficulties, this paper presents a new method for modeling and analyzing the system reliability based on dynamic evidential networks (DEN). This method allows modeling the influence of time and uncertainty on the failure and degradation of the system. The DEN graphical structure provides an easy way to specify the dependencies and, hence, to provide a compact representation of the system based on the Dempster Shafer theory. In addition, the DEN formalism is associated to simulation tools that enable an efficient processing for the models. A small system is used to compare the reliability estimations obtained by the proposed DEN model and those obtained by the classical Markov Chain.