Solving the Singularity Problem of Semiconductor Process Signal using Improved Dynamic Time Warping

In the micro process such as semiconductor process, Variation of variables directly affects the quality of the end product. So, it is important to monitor and manage the fluctuations in the variable. At this time, the signal is generated. However, the signal has a moving average and non-uniform variance, and different lengths in specific portion. Also it has a different total length. Recently, the DTW(Dynamic Time Warping) is used to coordinate of signal. However, the mean and variance of the signal is not uniform, there arises a problem that the singularity occurs. Singularity means unintuitive alignments that single point in time series connects onto a portion of another time series. To solve the problem that the singularity occurs, in this paper, we propose to use MODWT (Maximal Overlap Discrete Wavelet Transform) as a feature of signal and then calculate the warping path using divided matrices. We solve the singularity problem when applying the DTW to process the signal. Also, by comparing the result of applying process signal to DTW and proposed method, the proposed method is confirmed to be better than DTW in process signal.