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Belief reliability is a newly developed, model-based reliability metric which considers both what we know (expressed as reliability models) and what we don’t know (expressed as epistemic uncertainty in the reliability models) about the reliability. In this paper, we show that due to the explicit representation of epistemic uncertainty, belief reliability should not be regarded as a probability measure; rather, it should be treated as an uncertain measure in uncertainty theory. A minimal cut set-based method is developed to calculate the belief reliability of coherent systems. A numerical algorithm is, then, presented for belief reliability analysis based on fault tree models. The results of application show that the developed methods require less computations than the structure function-based method of classical reliability theory. [ABSTRACT FROM AUTHOR]

Due to the growing complexity of multi-state deteriorating systems and the lack of data, information and knowledge, epistemic uncertainty cannot be ignored anymore. Although there already exist some reliability metrics to deal with epistemic uncertainty problems in multi-state deteriorating systems, the final results provided by these methods are always probability intervals, which will suffer from the interval extension challenge in the subsequent operation. In this paper, we propose a reliability analysis method for the multi-state deteriorating system based on belief reliability theory, which can provide more conservative estimations and avoid interval extension problems. To describe the state transition process of multi-state deteriorating systems under the effect of epistemic uncertainty, a mathematical model called uncertain state transition chain is proposed. Under the framework of uncertainty theory, a total uncertainty inequality is given to assist the calculation of belief reliability. Using the proposed model and inequality, an algorithm of belief reliability for multi-state deteriorating systems considering the uncertainty of inspection time is provided. As a numerical example, the calculating process, the evaluation result and some discussions of a specific deteriorating system are given at last. [ABSTRACT FROM AUTHOR]