Multiscale monitoring of autocorrelated processes using wavelets analysis

This article proposes a new method to develop multiscale monitoring control charts for an autocorrelated process that has an underlying unknown ARMA(2, 1) model structure. The Haar wavelet transform is used to obtain effective monitoring statistics by considering the process dynamic characteristics in both the time and frequency domains. Three control charts are developed on three selected levels of Haar wavelet coefficients in order to simultaneously detect the changes in the process mean, process variance, and measurement error variance, respectively. A systematic method for automatically determining the optimal monitoring level of Haar wavelet decomposition is proposed that does not require the estimation of an ARMA model. It is shown that the proposed wavelet-based Cumulative SUM (CUSUM) chart on Haar wavelet detail coefficients is only sensitive to the variance changes and robust to process mean shifts. This property provides the separate monitoring capability between a variance change and a mean shift, which shows its advantage by comparison with the traditional CUSUM monitoring chart. For the purpose of mean shift detection, it is also shown that using the proposed wavelet-based Exponentially Weighted Moving Average (EWMA) chart to monitor Haar wavelet scale coefficients will more successfully detect small mean shifts than direct-EWMA charts.