Monitoring nonlinear profiles adaptively with a wavelet-based distribution-free CUSUM chart

Huizhu Wang, Seong Hee Kim, Xiaoming Huo, Youngmi Hur, James R. Wilson

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A wavelet-based distribution-free tabular CUSUM chart based on adaptive thresholding, WDFTCa is designed for rapidly detecting shifts in the mean of a high-dimensional profilewhose noise components have a continuous nonsingular multivariate distribution. First computing a discrete wavelet transform of the noise vectors for randomly sampled Phase I (in-control) profiles, WDFTCa uses a matrix-regularization method to estimate the covariance matrix of the wavelet-transformed noise vectors; then, those vectors are aggregated (batched) so that the non-overlapping batch means of the wavelet-transformed noise vectors have manageable covariances. Lower and upper in-control thresholds are computed for the resulting batch means of the wavelet-transformed noise vectors using the associated marginal Cornish-Fisher expansions that have been suitably adjusted for between-component correlations. From the thresholded batch means of the wavelet-transformed noise vectors, Hotelling's T2-type statistics are computed to set the parameters of a CUSUM procedure. To monitor shifts in the mean profile during Phase II (regular) operation, WDFTCa computes a similar Hotelling's T2-type statistic from successive thresholded batch means of the wavelet-transformed noise vectors using the in-control thresholds; thenWDFTCa applies the CUSUM procedure to the resulting T2-type statistics. Experimentation with several normal and non-normal test processes revealed that WDFTCa outperformed existing non-adaptive profile-monitoring schemes.

Original languageEnglish
Pages (from-to)4648-4667
Number of pages20
JournalInternational Journal of Production Research
Volume53
Issue number15
DOIs
Publication statusPublished - 2015 Aug 3

All Science Journal Classification (ASJC) codes

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

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