Mohamed Sallak

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.

An extension of Universal Generating Function in Multi-State Systems Considering Epistemic Uncertainties

Many practical methods and different approaches have been proposed to assess Multi-State Systems (MSS) reliability measures. The universal generating function (UGF) method, introduced in 1986, is known to be a very efficient way of evaluating the availability of different types of MSSs. In this paper, we propose an extension of the UGF method considering epistemic uncertainties. This extended method allows one to model ill-known probabilities and transition rates, or to model both aleatory and epistemic uncertainty in a single model. It is based on the use of belief functions which are general models of uncertainty. We also compare this extension with UGF methods based on interval arithmetic operations performed on probabilistic bounds.

Reliability assessment for multi-state systems under uncertainties based on the Dempster–Shafer theory

This article presents an original method for evaluating reliability indices for Multi-State Systems (MSSs) in the presence of aleatory and epistemic uncertainties. In many real- world MSSs, an insufficiency of data makes it difficult to estimate precise values for component state probabilities. The proposed approach applies the transferable belief model interpretation of the Dempster–Shafer theory to represent component state beliefs and to evaluate the MSS reliability indices. The example of an oil transmission system is used to demonstrate the proposed approach and it is compared with the universal generating function method. The value of the Dempster–Shafer theory lies in its ability to use several combination rules in order to evaluate reliability indices for MSSs that depend on the reliability of the experts’ opinions as well as their independence.

Transferable belief model for reliability analysis of systems with data uncertainties and failure dependencies

Abstract Dealing with uncertainty adds a further level of complexity to problems of reliability analysis. The uncertainties which impact reliability studies usually involve incomplete or imprecise reliability data and complex failure dependencies. This paper proposes an original methodology based on the transferable belief model (TBM) to include failure dependencies between components in the evaluation of the reliability of the whole system, given both epistemic and aleatory uncertainties. First, based on expert opinion and experimental data, basic probability assignments (BPAs) are assigned to reliability data components. TBM operations are then used to obtain the reliability of the whole system, for series, parallel, series–parallel, parallel–series, and bridge configurations. Implicit, explicit, and discounting approaches are presented for taking account of failure dependencies. Finally, the proposed model is applied to take into account common cause failures (CCFs) in a case study.

Modeling of ERTMS Level 2 as an SoS and Evaluation of its Dependability Parameters Using Statecharts

In this paper, we consider the European Rail Traffic Management System (ERTMS) as a System-of-Systems (SoS) and propose modeling it using Unified Modeling Language statecharts. We define the performance evaluation of the SoS in terms of dependability parameters and average time spent in each state (working state, degraded state, and failed state). The originality of this work lies in the approach that considers ERTMS Level 2 as an SoS and seeks to evaluate its dependability parameters by considering the unavailability of the whole SoS as an emergent property. In addition, human factors, network failures, Common-Cause Failures (CCFs), and imprecise failure and repair rates are taken into account in the proposed model.

An evidential network approach to support uncertain multiviewpoint abductive reasoning

The paper proposes an approach to support human abductive reasoning in the diagnosis of a multiviewpoint system. The novelty of this work lies on the capability of the approach to treat the uncertainty held by the agent performing the diagnosis. To do so, we make use of evidential networks to represent and propagate the uncertain evidence gathered by the agent. Using forward and backward propagation of the information, the impact of the evidence over the different symptoms and causes of failure is quantified. The agent can then make use of this information as additional hints in an iterative diagnosis process until a desired degree of certainty is obtained. The model is compared with a deterministic one in which evidence is represented by binary states, that is, a symptom is either observed or not.

An Efficient Method for Reliability Analysis of Systems Under Epistemic Uncertainty Using Belief Function Theory

We present an efficient method based on the inclusion-exclusion principle to compute the reliability of systems in the presence of epistemic uncertainty. A known drawback of belief functions and other imprecise probabilistic theories is that their manipulation is computationally demanding. Therefore, we investigate some conditions under which the measures of belief function theory are additive. If this property is met, the application of belief functions is more computationally efficient. It is shown that these conditions hold for minimal cuts and paths in reliability theory. A direct implication of this result is that the credal state (state of beliefs) about the failing (working) behavior of components does not affect the credal state about the working (failing) behavior of the system. This result is proven using a reliability analysis approach based on belief function theory. This result implies that the bounding interval of the systems reliability can be obtained with two simple calculations using methods similar to those of classical probabilistic approaches. A discussion about the applicability of the discussed theorems for non-coherent systems is also proposed.

Availability assessment of railway signalling systems with uncertainty analysis using Statecharts

In this paper, we propose an original simulation approach to evaluate the availability of systems in the presence of state uncertainty which arises from incompleteness or imprecision of knowledge and data. This approach is based on a simulation method combining the belief functions theory and the Statecharts. Then we propose a Statechart model of a railway signalling system, European Rail Traffic Management System (ERTMS) Level 2 considering state uncertainty, and evaluate its availability according to the RAMS requirements defined in the railway standards. Finally we propose a sensitivity analysis to estimate the state uncertainty of which constituent system has the most significant influence on the state uncertainty of the entire ERTMS Level 2.

Construction of Belief Functions From Statistical Data About Reliability Under Epistemic Uncertainty

Probability theory is well adapted to handle aleatory uncertainties resulting from the variability of failure phenomena. Recently, several uncertainty theories such as belief function theory were introduced in reliability assessments to handle epistemic uncertainties resulting from the lack of knowledge or insufficient data. In this paper, we propose some methods to construct belief functions of reliability parameters of components from statistical data about reliability. The proposed methods consider the parametric estimation of reliability parameters.

Inclusion-exclusion principle for belief functions

The inclusion-exclusion principle is a well-known property in probability theory, and is instrumental in some computational problems such as the evaluation of system reliability or the calculation of the probability of a Boolean formula in diagnosis. However, in the setting of uncertainty theories more general than probability theory, this principle no longer holds in general. It is therefore useful to know for which families of events it continues to hold. This paper investigates this question in the setting of belief functions. After exhibiting original sufficient and necessary conditions for the principle to hold, we illustrate its use on the uncertainty analysis of Boolean and non-Boolean systems in reliability.