A new approach to solve dynamic fault trees

Amari, Suprasad V.; Dill, Glenn; Howald, E.

doi:10.1109/rams.2003.1182018

Cited by 79 publications

(59 citation statements)

References 6 publications

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“…Close form expressions for the dynamic gates with any distribution function are given in (Amari et al (2003)). …”

Section: Probabilistic Analysis Of Pdftsmentioning

confidence: 99%

“…Given an event x with distribution function F x (t) and density function f x (t), the following expressions hold under the hypothesis of s-independence by extension of (Amari et al (2003);Fussel et al (1976)):…”

Section: Calculation Of the Failure Probability With Markov Chainsmentioning

confidence: 99%

“…The quantitative analysis of the DFT consists in exploding minimal modules (Dutuit and Rauzy (1996)) of dynamic gates into their state-space representation and computing numerically the related occurrence probability by means of a Continuous Time Markov Chain (Dugan et al (1992)), thus assuming exponential time-to-failure distributions. A new approach, able to include any probability distribution, has been presented in (Amari et al (2003)), where closed form expressions are determined as a function of the generic probability distributions of the basic events, and a numerical integration is proposed to solve them.…”

Section: Introductionmentioning

confidence: 99%

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

Merle

Roussel

Lesage

et al. 2009

IFAC Proceedings Volumes

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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.

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“…Close form expressions for the dynamic gates with any distribution function are given in (Amari et al (2003)). …”

Section: Probabilistic Analysis Of Pdftsmentioning

confidence: 99%

Section: Calculation Of the Failure Probability With Markov Chainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Merle

Roussel

Lesage

et al. 2009

IFAC Proceedings Volumes

View full text Add to dashboard Cite

show abstract

“…There are many algorithms applied to calculation of the probabilities of node accident and accident consequence of dynamic bow tie analysis: Hidden Markov Model, Bayesian Network (Khakzad et al 2013), Integral Algorithm (Amari et al 2003) and Monte Carlo Simulation (Kim et al 2016). In terms of simulated time and practicability, the Monte Carlo Simulation has an advantage over other methods.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Reliability Based Bow Tie Analysis of Coal Mine Water Inrush Risks

Zhang

Wang

Wei

2017

GREE

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Water inrush is a serious geological accident in underground coal mines. This paper focuses on the method of the bow tie analysis based on fuzzy reliability to assess the risk of water inrush in coal mines. First, post failure probability and repair probability of initiating events are divided into 5 levels. Then triangular fuzzy numbers are adopted to quantify experts' language and to acquire the reliability rate which close to the actual values by defuzzification and calculation. According to dynamic bow-tie analysis model, using the method of moments to fit the reliability time of events by Weibull distribution and offering the random sampling rule of failure and repair time for illustrating the feasibility of fuzzy reliability evaluation. To demonstrate the effectiveness of the proposed assessment approach, bow tie analysis model of water inrush in coal mines is taken as an example.

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“…Amari et al [5] propose a method to analyze dynamic fault trees in order to find the best strategy for avoiding or minimizing the state space explosion problem. The problem of efficient integration into the product development cycle, however is not solved following these methods.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Optimization and Assessment of Voting Strategies for X-by-Wire Systems

Kucera

Mauser

2007

Software Technologies for Embedded and Ubiquitous Systems

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Abstract. Signal voting of redundant sensor values and communication channels is of central importance in today's X-by-wire systems. The required degree of sensor redundancy, the type of redundancy, and finally the voting strategy must be designed to meet the system's dependability requirements. These design decisions depend on an analysis of the probabilities and effects of all underlying fault scenarios. Given a probabilistic fault model and a communication model, the voting step can be formally stated as a maximum-likelihood estimation of the correct input signal. With an example of an X-by-wire system we show how GTEFT can be used to derive the failure probabilities of different fault scenarios for various systems architectures and different voting strategies. Thus the capability of GTEFT to support system development and system assessment is demonstrated.

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A new approach to solve dynamic fault trees

Cited by 79 publications

References 6 publications

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

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

Fuzzy Reliability Based Bow Tie Analysis of Coal Mine Water Inrush Risks

Probabilistic Optimization and Assessment of Voting Strategies for X-by-Wire Systems

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