A Phase II predictive ratio CUSUM chart for normal data with cautious parameter learning for torque monitoring in the permanent magnet brakes

Monitoring the braking torque of permanent magnet brakes (PMBs) is crucial for ensuring the safety and reliability of industrial systems. However, traditional monitoring methods often lack sensitivity when Phase I data is limited, which can lead to delays in detecting braking torque degradation. To address this challenge, we propose an enhanced Phase II Predictive Ratio CUSUM (PRC) control chart for Normal data, integrating cautious parameter learning with Guaranteed In-Control Performance (GICP) design within a Bayesian framework, aiming specifically to detect persistent mean shifts. This approach facilitates real-time monitoring of braking torque in PMBs by effectively updating parameter estimates while minimizing the impact of out-of-control observations. Simulation results show that when Phase I data is scarce, the enhanced Phase II control chart outperforms its competitors in most mean-shift scenarios and remains competitive, particularly for moderate to large shifts, when larger Phase I samples are available. Finally, real torque data from PMBs is employed to demonstrate the implementation of the recommended scheme in the monitoring of braking torque.