Monitoring nonlinear profiles using a wavelet-based distribution-free CUSUM chart

Abstract

WDFTC is a wavelet-based distribution-free CUSUM chart for detecting shifts in the mean of a profile with noisy components. Exploiting a discrete wavelet transform (DWT) of the mean in-control profile, WDFTC selects a reduced-dimension vector of the associated DWT components from which the mean in-control profile can be approximated with minimal weighted relative reconstruction error. Based on randomly sampled Phase I (in-control) profiles, the covariance matrix of the corresponding reduced-dimension DWT vectors is estimated using a matrix-regularisation method; then the DWT vectors are aggregated (batched) so that the non-overlapping batch means of the reduced-dimension DWT vectors have manageable covariances. To monitor shifts in the mean profile during Phase II operation, WDFTC computes a Hotelling's T ²-type statistic from successive non-overlapping batch means and applies a CUSUM procedure to those statistics, where the associated control limits are evaluated analytically from the Phase I data. Experimentation with several normal and non-normal test processes revealed that WDFTC was competitive with existing profile-monitoring schemes.

Keywords:

• SPC
• quality control
• statistical methods
• profile
• CUSUM chart
• wavelet transform

Acknowledgements

The authors thank Dr Christina Staudhammer (University of Florida) and Dr Eric Chicken (Florida State University) for numerous enlightening discussions on this work. The authors also thank the Editors and referees for suggestions that improved the clarity and accessibility of this article.