Dirichlet Process Gaussian Mixture Models for Real-Time Monitoring and Their Application to Chemical Mechanical Planarization
The goal of this work is to use sensor data for online detection and identification of process anomalies (faults). In pursuit of this goal, we propose Dirichlet process Gaussian mixture (DPGM) models. The proposed DPGM models have two novel outcomes: 1) DP-based statistical process control (SPC) chart for anomaly detection and 2) unsupervised recurrent hierarchical DP clustering model for identification of specific process anomalies. The presented DPGM models are validated using numerical simulation studies as well as wireless vibration signals acquired from an experimental semiconductor chemical mechanical planarization (CMP) test bed. Through these numerically simulated and experimental sensor data, we test the hypotheses that DPGM models have significantly lower detection delays compared with SPC charts in terms of the average run length (ARL 1 ) and higher defect identification accuracies (F-score) than popular clustering techniques, such as mean shift. For instance, the DP-based SPC chart detects pad wear anomaly in CMP within 50 ms, as opposed to over 140 ms with conventional control charts. Likewise, DPGM models are able to classify different anomalies in CMP.