A Robust Control Chart Based on Wavelets for Preliminary Analysis of Individual Observations

A control chart based on wavelets for preliminary analysis of individual observations is proposed for detecting the shifts in the process mean. The basic motivation for our proposed method comes from the fact that the wavelets are able to detect the abnormal changes which may occur at multiple scales in a small number of relatively large wavelets coefficients. The chart proposed is preferable from a robustness point of view, has attractive detection performances and would be particularly useful in preliminary setting where we usually do not have knowledge of the underlying distribution.