I. Introduction
In a manufacturing plant, power plant or factory, various types of sensors are installed at various equipment of various processes to monitor the quality of the products, the progress of various processes, the condition of the output, etc. These sensors generate a huge volume of time-series waveform data. There are a number of characteristics of this huge volume of time-series waveform data. First, the time-series waveform data are of variable lengths. Second, a waveform may transit among multiple stationary states depending on various processes but on a stationary state the waveform may have fluctuations, and during these transitions, it may produce spikes, overshoots, and undershoots. Third, there may be a minute difference between an abnormal waveform and a normal waveform. Fourth, the number of abnormal waveforms may be very small compared to the huge volume of normal waveforms because in fabrication of semiconductor and storage products, anomaly rarely occurs in an equipment and if an anomaly occurs, counter-measures are enforced to prevent re-occurring of the same anomaly. An anomaly detection technique that can detect anomaly using this huge volume of time-series waveform data at high speed and high precision is needed.