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

作者：Wang Huizhu; Kim Seong Hee^*; Huo Xiaoming; Hur Youngmi; Wilson James R

来源：International Journal of Production Research, 2015, 53(15): 4648-4667.

DOI：10.1080/00207543.2015.1029085

• quality control
• high dimension
• profile
• CUSUM chart
• distribution-free
• discrete wavelet transform

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 profile whose 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 T-2-type statistics are computed to set the parameters of a CUSUM procedure. To monitor shifts in the mean profile during Phase II (regular) operation, T-2-type statistic from successive thresholded batch means of the wavelet-transformed noise vectors using the in-control thresholds; then WDFTCa applies the CUSUM procedure to the resulting T-2-type statistics. Experimentation with several normal and non-normal test processes revealed that WDFTCa outperformed existing non-adaptive profile-monitoring schemes.

• 出版日期2015-8-3