| Summary: | 碩士 === 元智大學 === 工業工程與管理學系 === 98 === In semiconductor manufacturing, the conduction of regression models on Wafer Acceptance Test (WAT) data plays a cornerstone to Fab-wide Process Control. Unfortunately, WAT data usually manifests multiple liner models, in which the model Indicator is usually a “hidden variable”. EM-Based Clusterwise Regression( EMCR) technique has been applied to the modeling of WAT data with multiple linear models. Though EMCR has been validated in few semiconductor manufacturing cases, the performance of EMCR degrades under two characteristics of WAT data: (1) high collinearity among explanatory variables in a WAT regression model, and (2) outliers in WAT data.
The characteristic of high collinearity will result in large variation of EMCR regression coefficient, which could further mislead the interpretation of EMCR regression coefficient. To remove the collinearity among explanatory variables, Principle Component Analysis (PCA) is integrated with EMCR and is named as PCA-Enhanced EMCR. Simulation studies show that PCA-Enhanced EMCR is 5 times better than EMCR in convergence quality,.
Though EMCR adopts the weighted regression technique, it cannot be free from the outlier impacts. In EMCR, for each data point, its weight for regression is set as its probabilistic membership with respect to individual regression models. Outlier may induce excessive estimation of probabilistic membership and therefore result in biased estimation of regression coefficients. To cope with the outlier, in addition to the probabilistic membership, a new weight resistant to outlier is designed to be part of the regression weight. The EMCR enhanced by double weighted method is called DW-EMCR. Simulation studies show that DW-EMCR not only improves the variation explanation ability of WAT regression model, but also improves the convergence efficiency of EMCR.
A data set in which collinearity and outlier characteristics coexist is collected from a semiconductor foundry for validations. Due to the fact that the true model is unknown, the re-sampling technique is applied for performance evaluation. For the collinearity problem, the technique of PCA-Enhanced EMCR which conducts PCA on highly correlated variables indeed performs better than EMCR. For the outlier problem, DW-EMCR demonstrates it capability on improving the statistical confidence interval of regression coefficients, which further helps engineer discover the important factor masked by outlier.
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