In this paper, a systematic review of non-probabilistic reliability metrics is conducted to assist the selection of appropriate reliability metrics to model the influence of epistemic uncertainty. Five frequently used non-probabilistic reliability metrics are critically reviewed, i.e., evidence-theory-based reliability metrics, interval-analysis-based reliability metrics, fuzzy-interval-analysis-based reliability metrics, possibility-theory-based reliability metrics (posbist reliability) and uncertainty-theory-based reliability metrics (belief reliability). It is pointed out that a qualified reliability metric that is able to consider the effect of epistemic uncertainty needs to (1) compensate the conservatism in the estimations of the component-level reliability metrics caused by epistemic uncertainty, and (2) satisfy the duality axiom, otherwise it might lead to paradoxical and confusing results in engineering applications. The five commonly used non-probabilistic reliability metrics are compared in terms of these two properties, and the comparison can serve as a basis for the selection of the appropriate reliability metrics

In this article, we develop a mixture of Gaussians-evidential hidden Markov model (MoG-EHMM) to fuse expert knowledge and condition monitoring information for remaining useful life (RUL) prediction under the belief function theory framework. The evidential expectation-maximization algorithm is implemented in the offline phase to train the MoG-EHMM based on historical data. In the online phase, the trained model is used to recursively update the health state and reliability of a particular individual system. The predicted RUL is, then, represented in the form of its probability mass function. A numerical metric is defined based on the Bhattacharyya distance to measure the RUL prediction accuracy of the developed methods. We applied the developed methods on a simulation experiment and a real-world dataset from a bearing degradation test. The results demonstrate that despite imprecisions in expert knowledge, the performance of RUL prediction can be substantially improved by fusing expert knowledge with condition monitoring information.