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 ( ${k}$ NNs) is effective for fault detection of processes with multimode characteristics. When the variance structures of different mode data sets are similar, ${k}$ NN 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 ${k}$ NN. The main reason is that ${k}$ NN 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 ${k}$ NN, a new fault detection strategy based on weighted distance of ${k}$ NNs (FD- $\text{w}{k}$ NNs) is proposed. In FD- $\text{w}{k}$ NN, the weighted parameter of distance of a sample to its $j $ th nearest neighbor is the reciprocal of the mean distance of the ${j}$ th nearest neighbor to its ${k}$ nearest neighbors. Compared with the statistic in ${k}$ NN, the new statistic in FD- $\text{w}{k}$ NN can both eliminate the influence of variance structure in multimodal processes and reduce the autocorrelation of statistic values. As a single model method, FD- $\text{w}{k}$ NN is more suitable for monitoring multimode processes than ${k}$ NN. The efficiency of FD- $\text{w}{k}$ NN is implemented in a simulated multimode case and in the semiconductor manufacturing processes. The experimental results indicate that the proposed method outperforms FD- ${k}$ NN, principal component analysis (PCA) and kernel PCA.