Wavelet-based multiscale statistical process monitoring: A literature review

Data that represent complex and multivariate processes are well known to be multiscale due to the variety of changes that could occur in a process with different localizations in time and frequency. Examples of changes may include mean shift, spikes, drifts and variance shifts all of which could occur in a process at different times and at different frequencies. Acoustic emission signals arising from machining, images representing MRI scans and musical audio signals are some examples that contain these changes and are not suited for single scale analysis. The recent literature contains several wavelet-decomposition-based multiscale process monitoring approaches including many real life process monitoring applications. These approaches are shown to be effective in handling different data types and, in concept, are likely to perform better than existing single scale approaches. There also exists a vast literature on the theory of wavelet decomposition and other statistical elements of multiscale monitoring methods, such as principal components analysis, denoising and charting. To our knowledge, no comprehensive review of the work relevant to multiscale monitoring of both univariate and multivariate processes has been presented to the literature. In this paper, over 150 both published and unpublished papers are cited for this important subject, and some extensions of the current research are also discussed.