Guillaume Merle

Probabilistic Algebraic Analysis of Fault Trees With Priority Dynamic Gates and Repeated Events

This paper focuses on a sub-class of Dynamic Fault Trees (DFTs), called Priority Dynamic Fault Trees (PDFTs), containing only static gates, and Priority Dynamic Gates (Priority-AND, and Functional Dependency) for which a priority relation among the input nodes completely determines the output behavior. We define events as temporal variables, and we show that, by adding to the usual Boolean operators new temporal operators denoted BEFORE and SIMULTANEOUS, it is possible to derive the structure function of the Top Event with any cascade of Priority Dynamic Gates, and repetition of basic events. A set of theorems are provided to express the structure function in a sum-of-product canonical form, where each product represents a set of cut sequences for the system. We finally show through some examples that the canonical form can be exploited to determine directly and algebraically the failure probability of the Top Event of the PDFT without resorting to the corresponding Markov model. The advantage of the approach is that it provides a complete qualitative description of the system, and that any failure distribution can be accommodated.

Quantitative Analysis of Dynamic Fault Trees based on the Structure Function

This paper presents a probabilistic model of dynamic gates which allows to perform the quantitative analysis of any Dynamic Fault Tree (DFT) from its structure function. Both these probabilistic models and the quantitative analysis which can be performed thanks to them can accommodate any failure distribution of basic events. We illustrate our approach on a DFT example from the literature.

Algebraic determination of the structure function of Dynamic Fault Trees

This paper presents an algebraic framework allowing to algebraically model dynamic gates and determine the structure function of any Dynamic Fault Tree (DFT). This structure function can then be exploited to perform both the qualitative and quantitative analysis of DFTs directly, even though this latter aspect is not detailed in this paper. We illustrate our approach on a DFT example from the literature.

Quantitative Analysis of Dynamic Fault Trees Based on the Coupling of Structure Functions and Monte Carlo Simulation

This paper focuses on the quantitative analysis of Dynamic Fault Trees (DFTs) by means of Monte Carlo simulation. In a previous article, we defined an algebraic framework allowing to determine the structure function of DFTs. We exploit this structure function and the minimal cut sequences that it allows to determine, to know the failure mode configuration of the system, which is an input of Monte Carlo simulation. We show that the results obtained are in good accordance with theoretical results and that some results, such as importance measures and sensitivity indexes, are not provided by common quantitative analysis and yet interesting. We finally illustrate our approach on a DFT example from the literature. Copyright

Dynamic fault tree analysis based on the structure function

This paper presents an algebraic approach allowing to perform the analysis of any Dynamic Fault Tree (DFT). This approach is based on the ability to formally express the structure function of DFTs. We first present the algebraic framework that we introduced to model dynamic gates and he nce be able to determine the structure function of DFTs. Then, we show that this structure function can be rewritten under a canonical form from which the qualitative analysis of DFTs can be performed directly. We finally provide a probabilistic model of dynamic gates to be able to perform the quantitative analysis of DFTs from their structure function.

ALGEBRAIC MODELLING OF FAULT TREES WITH PRIORITY AND GATES

Abstract This paper presents a formal framework allowing to extend the simplification of static fault trees to fault trees built with gates PRIORITY AND. The laws which make these simplifications possible have been demonstrated thanks to a homogeneous algebraic definition of each gate studied. These definitions use a mathematical model of events able to take into account their order of appearance. The processing of an example points out the possibilities offered by this algebraic framework dedicated to non-repairable faults.

Algebraic Expression of the Structure Function of a subclass of Dynamic Fault Trees

This paper focuses on a subclass of Dynamic Fault Trees (DFTs), called Priority Dynamic Fault Trees (PDFTs), containing only static gates and Priority Dynamic Gates (PAND and FDEP) for which a priority relation among the input nodes completely determines the output behavior. We define events as temporal variables and we show that, by adding to the usual Boolean operators new temporal operators denoted BEFORE and SIMULTANEOUS, it is possible to derive the structure function of the Top Event with any cascade of Priority Dynamic Gates and repetition of basic events. A set of theorems are provided to express the structure function in a sum-of-product canonical form. We finally show through an example that the canonical form can be exploited in order to determine directly and algebraically the failure probability of the Top Event of the PDFT without resorting to the corresponding Markov model. The advantage of this approach is that it provides a complete qualitative description of the system and that any failure distribution can be accommodated.