Fault Detection Using Random Projections and k-Nearest Neighbor Rule for Semiconductor Manufacturing Processes

Fault detection technique is essential for improving overall equipment efficiency of semiconductor manufacturing industry. It has been recognized that fault detection based on k nearest neighbor rule (kNN) can effectively deal with some characteristics of semiconductor processes, such as multimode batch trajectories and nonlinearity. However, the computation complexity and storage space involved in neighbors searching of k NN prevent it from online monitoring, especially for high dimensional cases. To deal with this difficulty, principal component-based k NN has also been presented in literature, in which dimension reduction is done by principal component analysis (PCA) before k NN rule implemented to fault detection. However, dimension reduction by PCA may distort the distances between pairs of samples (trajectories). Thus the false alarm and missing detection of k NN for fault detection may increase in principal component subspace because PCA fails to preserve pairwise distances in subspace. To overcome this drawback, we propose a new fault detection method based on random projection and k NN rule, which combines the advantages of random projection in distance preservation (in the expectation) and k NN rule in dealing with the problems of multimodality and nonlinearity that often coexist in semiconductor manufacturing processes. An industrial example illustrates the performance of the proposed method.