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 (ARL1) 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. Note to Practitioners-This paper forwards novel Dirichlet process Gaussian mixture (DPGM) models for online process quality monitoring. The practical outcome is that the deleterious impact of process drifts on product quality is identified in their early stages using the presented DPGM models. For instance, sensor signal patterns from contemporary advanced manufacturing processes rarely follow distribution symmetry or normality assumptions endemic to traditional statistical process control (SPC) methods. These assumptions limit the effectiveness of traditional SPC methods for detection of process anomalies from complex heterogeneous sensor data. In comparison, the proposed DP-based SPC is capable of detecting process changes in the sensor data notwithstanding the characteristics of the underlying distributions. Moreover, we show that the recurrent hierarchical DP clustering model identifies process anomalies with higher fidelity compared with traditional methods, such as mean shift clustering.