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Dealing with uncertainty introduces an increased level of complexity to reliability analysis problems. The uncertainties associated to reliability studies usually arise from the difficulty to account for incomplete or imprecise reliability data and complex failure dependencies. This paper introduces the Transferable Belief Model (TBM) to the reliability analysis so that epistemic uncertainties can be taken into account as well as aleatory uncertainties. Two approaches are used to represent failure dependencies of components: an implicit and an explicit approach. The TBM model is then compared to an intervalprobability model by highlighting the different characteristics of the results obtained.

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In this paper, extended component importance measures (Birnbaum importance, RAW, RRW and Criticality importance) considering aleatory and epistemic uncertainties are introduced. The D-S theory which is considered to be a less restricted extension of probability theory is proposed as a framework for taking into account both aleatory and epistemic uncertainties. The epistemic uncertainty defined in this paper is the total lack of knowledge of the component state. The objective is to translate this epistemic uncertainty to the epistemic uncertainty of system state and to the epistemic uncertainty of importance measures of components. The Affine Arithmetic allows us to provide much tighter bounds in the computing process of interval bounds of importance measures avoiding the error explosion problem. The efficiency of the proposed measures is demonstrated using a bridge system with different types of reliability data (aleatory uncertainty, epistemic uncertainty and experts' judgments). The influence of the epistemic uncertainty on the components' rankings is described. Finally, a case study of a fire-detector system located in a production room is provided.A comparison between the proposed measures and the probabilistic importance measures using two-stage Monte Carlo simulations is also made.

This paper 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 (TBM) interpretation of the Dempster-Shafer theory to represent component state beliefs and to evaluate the MSS reliability indices. We use the example of an oil transmission system to demonstrate the proposed approach and we compare it 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. KEY WORDSMulti-State System (MSS), reliability indices, Dempster-Shafer (D-S) theory, Transferable Belief Model (TBM), Experts' opinion.

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