Improved Shewhart Chart Using Multiscale Representation

Abstract

Most univariate process monitoring techniques operate under three main assumptions, that the process residuals being evaluated are Gaussian, independent and contain a moderate level of noise. The performance of the conventional Shewhart chart, for example, is adversely affected when these assumptions are violated. Multiscale wavelet-based representation is a powerful data analysis tool that can help better satisfy these assumptions, i.e., decorrelate autocorrelated data, separate noise from features, and transform the data to better follow a Gaussian distribution at multiple scales.

This research focused on developing an algorithm to extend the conventional Shewhart chart using multiscale representation to enhance its performance. Through simulated synthetic data, the developed multiscale Shewhart chart showed improved performance (with lower missed detection and false alarm rates) than the conventional Shewhart chart.

The developed multiscale Shewhart chart was also applied to two real world applications, simulated distillation column data, and genomic copy number data, to illustrate the advantage of using the multiscale Shewhart chart for process monitoring over the conventional one.