Multiscale Statistical Process Control Using Wavelet Packets

An approach is presented for conducting multiscale statistical process control (MSSPC), based on a library of basis functions provided by wavelet packets. The proposed approach explores the improved ability of wavelet packets in extracting features with arbitrary locations, and having different localizations in the time-frequency domain, in order to improve the detection performances achieved with wavelet-based MSSPC. A novel approach is also developed for adaptively selecting the best decomposition depth. Such an approach is described in detail and tested using artificial simulated signals, employed to compare average run length (ARL) performance against other SPC methodologies. Furthermore, its performance under real world situations is also assessed, for two industrial case studies using datasets containing process upsets, through the construction of receiver operating characteristic (ROC) curves. Both univariate and multivariate cases are covered. ARL results for a step perturbation show that the proposed methodology presents a steady good performance for all shift magnitudes, without significantly changing its relative scores, as happens with other current methods, whose relative performance depends on the shift magnitude being tested. For artificial disturbances, with features localized in the time/frequency domain, multiscale methods do present the best performance, and for the particular case of detecting a decrease in autocorrelation they are the only ones that can detect such a perturbation. In the examples using industrial datasets, where disturbances exhibit more complex patterns, multiscale approaches also present the best results, in particular in the range of low false alarms, where monitoring methods are aimed to operate. 2008 American Institute of Chemical Engineers AIChE J, 54: 2366–2378, 2008