Degradation modeling considering multiple performance parameters degradation based on mixed effects models

With the rapid evolution of prognostics and health management, reliability models now require higher accuracy and extrapolation capabilities. Despite advances in measurement technology, a certain degree of measurement error remains inevitable. Additionally, material variability and equipment inaccuracies during manufacturing lead to initial product values that follow a distribution correlated with degradation rates. Significant differences in degradation rates are also observed under various stress combinations. Furthermore, competing failure relationships among different performance parameters make it insufficient to consider only a single parameter. To address these challenges, this paper introduces a novel nonlinear mixed-effects model that accounts for both measurement errors and stochastic effects from random initial conditions. The model efficiently captures the coupling among stress factors and the competing failure relationships among multiple performance parameters. Model parameters are estimated using the least squares method. Finally, the proposed model was verified through degradation test data obtained from electrolytic capacitors subjected to combined temperature and voltage stresses. The results demonstrate that incorporating multiple performance parameters enables a more accurate representation of the degradation process and significantly improves prediction performance compared with single-parameter approaches. Furthermore, the reliability function derived from the model effectively characterizes the probability of failure over time, validating the model's capability to capture long-term reliability behavior. This degradation model can be widely applied to various components and shows considerable potential for system-level degradation analysis.