Degradation process modeling and data-driven lifetime prediction for BGA specimen during small sample electromigration test

Electromigration (EM) poses a critical threat to Ball Grid Array (BGA) reliability, yet its lifetime prediction is challenged by limited and heterogeneous data. To address the limitation, this study develops a hybrid physics-informed uncertainty modeling framework for predicting BGA lifetime under small sample conditions. Electromigration experiments at three temperature-current stress levels confirmed copper redistribution layer (Cu RDL) narrowing as the dominant degradation mechanism. Based on this insight, the proposed model couples a simplified degradation formulation derived from relative resistance change with an uncertain differential equation (UDE) to quantify epistemic uncertainty, enabling belief reliable life estimation for individual specimens. Furthermore, a data analysis method for lifetime prediction integrating the Weibull uncertainty distribution, uncertain measure consistency, and Black equation extends lifetime prediction across operating conditions and ensures robustness under sparse data. Comparative analyses with other process-based degradation models and traditional lifetime prediction method based on regression-Weibull-Black equation show that the proposed method achieves superior fitting accuracy, improved stability of current and thermal sensitivities, and more conservative MTBF estimates. These findings highlight the method’s potential to support reliability-oriented design and preventive maintenance planning for high performance electronic packaging.