New control charts for monitoring univariate autocorrelated processes and high-dimensional profiles

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Lee, Joongsup
Kim, Seong-Hee
Wilson, James R.
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In this thesis, we first investigate the use of automated variance estimators in distribution-free statistical process control (SPC) charts for univariate autocorrelated processes. We introduce two variance estimators---the standardized time series overlapping area estimator and the so-called quick-and-dirty autoregressive estimator---that can be obtained from a training data set and used effectively with distribution-free SPC charts when those charts are applied to processes exhibiting nonnormal responses or correlation between successive responses. In particular, we incorporate the two estimators into DFTC-VE, a new distribution-free tabular CUSUM chart developed for autocorrelated processes; and we compare its performance with other state-of-the-art distribution-free SPC charts. Using either of the two variance estimators, the DFTC-VE outperforms its competitors in terms of both in-control and out-of-control average run lengths when all the competing procedures are tested on the same set of independently sampled realizations of selected autocorrelated processes with normal or nonnormal noise components. Next, we develop WDFTC, a wavelet-based distribution-free CUSUM chart for detecting shifts in the mean of a high-dimensional profile with noisy components that may exhibit nonnormality, variance heterogeneity, or correlation between profile components. A profile describes the relationship between a selected quality characteristic and an input (design) variable over the experimental region. 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-regularization method; then the DWT vectors are aggregated (batched) so that the nonoverlapping 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-square--type statistic from successive nonoverlapping batch means and applies a CUSUM procedure to those statistics, where the associated control limits are evaluated analytically from the Phase I data. We compare WDFTC with other state-of-the-art profile-monitoring charts using both normal and nonnormal noise components having homogeneous or heterogenous variances as well as independent or correlated components; and we show that WDFTC performs well, especially for local shifts of small to medium size, in terms of both in-control and out-of-control average run lengths.
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