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A statistical approach for monitoring solder joint quality is presented in this paper. In semiconductor manufacturing, there are often multiple independent root causes (variability sources) that contribute to the overall observed variability in the measured profile. Each variability source may result in a distinct spatial pattern across some of the measured product characteristics. A combinational blind source separation method is proposed to recognize these patterns based on a high-order statistical analysis of inspection data. Visualization of the resulting patterns is shown to help illustrate the nature of their root causes. For the identified individual variability sources, we apply autocorrelation exponentially weighted moving average control charts to monitor the mean shifts by accommodating their autocorrelation and non-Gaussian distributions. The proposed control chart also facilitates online monitoring of solder joint quality by avoiding the sophisticated time-series modeling.