Walid Mechri

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.

Uncertainty evaluation of Safety Instrumented Systems by using Markov chains

In this article, the problem of imprecision in assessing the performance of Safety Instrumented Systems (SIS) using fuzzy Markov chains is adressed. The scalar elementary probabilities usually considered in Markov chains are replaced by fuzzy numbers. It allows experts to express their uncertainty concerning the basic parameters of systems (common cause factors, failure rate ...) and, to evaluate the impact of the uncertainty. We show how the imprecision induces significant changes on the Safety Integrity Level (SIL) of a SIS. The proposed method ensures the relevance of the results. It is affirmed by the comparison with results obtained by a Monte Carlo sampling approach.

Unavailability evaluation of system by using Bayesian Network and fuzzy logic

In this article, the analysis of the problem of imprecision is treated in the evaluation of the unavailability of the Safety Instrumented Systems (SIS). The analysis rests on an approach by the Bayesian Networks; the imprecision on the characteristic parameters is modeled by an approach based on a fuzzy system of inference. The model suggested is applied to a SIS to evaluate the impact of the imprecision to the unavailability of the safety systems.

Bayesian network and probability boxes to analyze uncertainty in unavailability assessment

In this article the problem of uncertainty in assessing unavailability of Safety Instrumented Systems (SIS) is treated. The characteristic parameters of the SIS including Common Cause Failure (CCF) factors are replaced by probability densities families (p-boxes) allowing in reliability experts to express their uncertainty on the statement of values probabilities. We show how the imprecision is modeled and propagated in a Bayesian Networks which induces uncertainty about the failure probability on demand of the SIS and its Safety Integrity Level (SIL). We will demonstrate how the uncertainty on some characteristic parameters values causes significant variations on the level risk.

Fuzzy Bayesian network to model safety systems performance

This article, targets the problem of uncertainty in assessing unavailability of systems, using fuzzy Bayesian networks. The elementary probabilities usually considered in Bayesian networks are replaced by fuzzy numbers. It allows experts to express their uncertainty about the basic parameters of systems and to evaluate the impact of the uncertainty on the safety systems performance. We will demonstrate how the uncertainty on some characteristic parameters values causes significant variations on the systems unavailability. In order to highlight the comparison and to show the exactness of the approach, we propose a Monte Carlo sampling approach where we consider triangular probability distribution of common cause failures factors.