2010 # Transferable belief model for reliability analysis of systems with data uncertainties and failure dependencies

**Abstract:** 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…

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“…The second point of evidence theory is that belief measures of uncertainty may be assigned to overlapping sets and subsets of hypotheses, events or propositions as well as to individual hypothesis. D-S theory which can be considered as an alternative approach to represent uncertainties has gained an increasing amount of attention both from the theoretical and the applied point of view [30], [31], [32], [33]. In a finite discrete space, D-S theory is a generalization of probability theory where probabilities are assigned to sets instead of mutually exclusive singletons.…”

confidence: 99%

“…The second point of evidence theory is that belief measures of uncertainty may be assigned to overlapping sets and subsets of hypotheses, events or propositions as well as to individual hypothesis. D-S theory which can be considered as an alternative approach to represent uncertainties has gained an increasing amount of attention both from the theoretical and the applied point of view [30], [31], [32], [33]. In a finite discrete space, D-S theory is a generalization of probability theory where probabilities are assigned to sets instead of mutually exclusive singletons.…”

confidence: 99%

“…Nevertheless, there is very few works concerning the construction of BBAs [41], [33]. The problem of elicitation of experts' judgments has long been addressed in the probability theory framework related to reliability and risk assessments.…”

confidence: 99%

“…40 In recent years, the belief functions theory was used by many researchers in order to quantify the uncertainty in reliability and risk assessment studies. 34,35,[41][42][43][44][45] …”

confidence: 99%

“…Dempster-Shafer (D-S) theory, which can be considered as an alternative approach to represent uncertainties, has gained an increasing amount of attention both from the theoretical and the applied point of view. [32][33][34][35] In a finite discrete space, D-S theory is a generalization of probability theory where probabilities are assigned to sets instead of mutually exclusive singletons. This theory is still a young field compared with other theories and its main application is data fusion.…”

confidence: 99%

“…In their work, an OR gate was added explicitly to connect the original failure event in the FT model and the propagated failure events affected by the original failure event; then, these FT models are transformed into BDDs to evaluate the system unreliability. Sallak et al proposed explicit and implicit transferable belief model–based methods to analyze propagated failures (also called failure dependencies between components) in systems considering both epistemic and aleatory uncertainties. In their work, uncertainties related to reliability data were represented and propagated by belief functions theory, and propagated failures were represented by conditional basic probability assignments.…”

confidence: 99%