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

Joongsup Jay Lee, Youngmi Hur, Seong Hee Kim, James R. Wilson

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)6574-6594
Number of pages21
JournalInternational Journal of Production Research
Issue number22
Publication statusPublished - 2012 Nov 15

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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