Reliability assessment and hierarchical tolerance design for electromagnetic relay based on the distribution of a key process parameter

Electromagnetic relays (EMR) are the core control component in many equipment, and their reliability directly determines the operational stability and task execution capability of the entire system. Current degradation modeling primarily uses a single physics-of-failure (PoF) model, which cannot accurately characterize EMRs' multiple failure mechanisms. Furthermore, existing reliability analysis and optimization methods overlook the individual variability caused by manufacturing, making them unsuitable for EMRs with complex assembly processes. To address these limitations, a degradation modeling method integrating dual PoF models and considering the influence of key process parameters is proposed. This study focuses on EMRs failing due to excessive pick-up time, analyzes the failure mechanisms using a digital model first, and develops PoF models for both stress relaxation and electrical erosion. Second, to comprehensively characterize EMRs' pick-up time degradation behavior, a dual PoF-based accelerated degradation model is proposed. The model parameters are subsequently identified through the Expectation-Maximization algorithm. Third, a reliability model considering the distribution of contact pressure is derived to reflect manufacturing-induced individual variability. Further, a hierarchical tolerance design method is proposed to improve reliability from the manufacturing perspective. Finally, experimental results demonstrate that the proposed method reduces the degradation ratio of pick-up time by 25.3 %, effectively improving reliability.