Abstract: A method and apparatus for detecting performance of an apparatus for punching holes in a substrate, ensuring hole quality and/or minimizing or eliminating damage to the films during the hole punching process.

Abstract: A method for predicting extreme changes in numeric time series data includes converting a numeric time series into a sequence of symbols. A prediction method, such as a neural network or nearest neighbor algorithm is used to make the forecast. A numeric time series data is identified with extreme changes in them, and a window of length W that precedes the extreme change is extracted. Those extracts of a time series are built into a matrix (characteristic matrix) for singular value decomposition. The built matrix undergoes singular value decomposition, which reveals the characteristic vectors (symbols) that are indicative of time series that have characteristics that precede an extreme event. To perform forecasting, a window of length W in a new time series is generated and the dot product of the windows is taken against a predetermined number of columns of characteristic matrix, and, forecasting is performed on the new series.