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Evidential reasoning (ER) rule has been widely used in addressing uncertainty, ignorance, and vagueness information. To explore its performance measure (PM), the perturbation analysis (PA) for the ER rule (ER rule-PA) is conducted, with perturbation taken into consideration. This article aims to analyze the robustness and stability of the ER rule, serving as theoretical basis and technical support for applied research and applications. The combination of two pieces of independent evidence is discussed, and perturbation is added to one piece of evidence. To represent the expected utility of evidence combination under perturbation, perturbation utility is introduced. The novel concept of perturbation coefficient is proposed to characterize the PM of the ER rule (ER rule-PM). The properties of perturbation coefficient are explored to demonstrate the impact of perturbation. The maximum permissible error (MPE) of perturbation coefficient is defined to characterize the acceptability of perturbation. A numerical study is examined to illustrate the implementation process of ER rule-PA. Moreover, a case study of reliability evaluation of aerospace relay is conducted to show the potential applications of ER rule-PA, which makes the proposed method more practical. [ABSTRACT FROM AUTHOR]

Recently, a novel prediction model based on the evidential reasoning (ER) approach is developed to forecast reliability in engineering systems. In order to determine the parameters of the ER-based prediction model, some optimization models have been proposed to train the ER-based prediction model. However, these models are implemented in an offline fashion and thus it is very expensive to train and retrain them when new information is available. This correspondence paper is concerned with developing the recursive algorithms for updating the ER-based prediction model from the probability-based point of view. Using the recursive expectation maximization algorithm, two recursive algorithms are proposed for updating the parameters of the ER-based prediction model under judgmental and numerical outputs, respectively. As such, the proposed algorithms can be used to fine tune the ER-based prediction model online once new information becomes available. We verify the proposed method via a realistic example with missile reliability data. [ABSTRACT FROM PUBLISHER]