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Fault tree analysis (FTA), as one of the powerful tools in reliability engineering, has been widely used to enhance system quality attributes. In most fault tree analyses, precise values are adopted to represent the probabilities of occurrence of those events. Due to the lack of sufficient data or imprecision of existing data at the early stage of product design, it is often difficult to accurately estimate the failure rates of individual events or the probabilities of occurrence of the events. Therefore, such imprecision and uncertainty need to be taken into account in reliability analysis. In this paper, the evidential networks (EN) are employed to quantify and propagate the aforementioned uncertainty and imprecision in fault tree analysis. The detailed conversion processes of some logic gates to EN are described in fault tree (FT). The figures of the logic gates and the converted equivalent EN, together with the associated truth tables and the conditional belief mass tables, are also presented in this work. The new epistemic importance is proposed to describe the effect of ignorance degree of event. The fault tree of an aircraft engine damaged by oil filter plugs is presented to demonstrate the proposed method.

Evidential Networks for Fault Tree Analysis with Imprecise Knowledge