Statistical Process Control Based on Multi-scale Wavelets Analysis

Conventional control charts are based on the statistical assumption that measurements are independent and identically distributed. In industry applications, however, observations are autocorrelated due to the inherent cause of the process. Thus traditional methods will be inappropriate for autocorrelated process monitoring. In this paper, multi-scale wavelets analysis is introduced to autocorrelated processes. Process monitoring is reached by integrating Shewhart control chart with multi-scale wavelets analysis. Finally, Take ARMA (1,1) process for example. Monte carlo simulations about step-type or trend-type fault in autocorrelated processes are performed to explain the ARL property of the multi-scale SPC monitoring method. In addition, we also consider the performance of control charts and the relationship between the average run length (ARL) performance and wavelet decomposition depth.