Fault Detection Strategy Based on Weighted Distance of $k$ Nearest Neighbors for Semiconductor Manufacturing Processes

It has been recognized that the k nearest neighbors rule (kNNs) is effective for fault detection of processes with multimode characteristics. When the variance structures of different mode data sets are similar, kNN can indeed detect faults accurately. However, once the variance structures change markedly, some weak faults deviating from a dense mode fail to be detected using kNN. The main reason is that kNN statistic values of these weak faults are usually submerged by those of normal samples in some sparse modes. In order to overcome the above shortcomings of kNN, a new fault detection strategy based on weighted distance of kNNs (FD-wkNNs) is proposed. In FD-wkNN, the weighted parameter of distance of a sample to its jth nearest neighbor is the reciprocal of the mean distance of the jth nearest neighbor to its k nearest neighbors. Compared with the statistic in kNN, the new statistic in FD-wkNN can both eliminate the influence of variance structure in multimodal processes and reduce the autocorrelation of statistic values. As a single model method, FD-wkNN is more suitable for monitoring multimode processes than kNN. The efficiency of FD-wkNN is implemented in a simulated multimode case and in the semiconductor manufacturing processes. The experimental results indicate that the proposed method outperforms FD-kNN, principal component analysis (PCA) and kernel PCA.