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 journalArticle

18 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)6574-6594
Number of pages21
JournalInternational Journal of Production Research
Volume50
Issue number22
DOIs
Publication statusPublished - 2012 Nov 15

Fingerprint

Discrete wavelet transforms
Monitoring
Statistics
Covariance matrix
Wavelets
Cumulative sum
Charts
Distribution-free
Wavelet transform

All Science Journal Classification (ASJC) codes

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

Cite this

Lee, Joongsup Jay ; Hur, Youngmi ; Kim, Seong Hee ; Wilson, James R. / Monitoring nonlinear profiles using a wavelet-based distribution-free CUSUM chart. In: International Journal of Production Research. 2012 ; Vol. 50, No. 22. pp. 6574-6594.
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Monitoring nonlinear profiles using a wavelet-based distribution-free CUSUM chart. / Lee, Joongsup Jay; Hur, Youngmi; Kim, Seong Hee; Wilson, James R.

In: International Journal of Production Research, Vol. 50, No. 22, 15.11.2012, p. 6574-6594.

Research output: Contribution to journalArticle

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