A reliability evaluation method for electromagnetic relays based on a novel degradation-threshold-shock model with two-sided failure thresholds

•The joint effect of degradation and shocks is considered for electromagnetic relays.•A degradation-threshold-shock model with two-sided failure thresholds is proposed.•An analytical log-likelihood function is derived to estimate the model parameters.•Three reliability approximation methods are proposed to evaluate reliability.•A real case study shows the effectiveness of the proposed method. Electromagnetic relays are widespread in modern technological systems. It is imperative to accurately evaluate their reliability, so that operation and maintenance activities can be appropriately planned to guarantee the safe and stable operation of the system. However, the existing reliability evaluation methods for relays neglect welding phenomena, which can be viewed as shocks negatively affecting reliability. Moreover, the existing degradation-threshold-shock (DTS) models assume a one-sided failure threshold, but relays have two-sided thresholds according to their special failure mechanism. Thus, the evaluation methods may overestimate reliability, and the DTS models are inapplicable. To solve these problems, a DTS model with two-sided failure thresholds is proposed with the consideration of multi-source uncertainties to capture the failure mechanism of relays. A maximum likelihood estimation method for the model parameters is proposed via the moment generating function, the limit analysis, and the formula of conditional probability. Furthermore, lower and upper bounds of reliability are derived through the event analysis, and three approximation methods are proposed based on Monte Carlo simulations, the neglect of correlation, and several means of the bounds, respectively. Finally, a real case is used to compare the proposed method with the existing methods to show the effectiveness of the proposed method.