Statistical selection and wavelet-based profile monitoring

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Wang, Huizhu
Kim, Seong-Hee
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This thesis consists of two topics: statistical selection and profile monitoring. Statistical selection is related to ranking and selection in simulation and profile monitoring is related to statistical process control. Ranking and selection (R&S) is to select a system with the largest or smallest performance measure among a finite number of simulated alternatives with some guarantee about correctness. Fully sequential procedures have been shown to be efficient, but their actual probabilities of correct selection tend to be higher than the nominal level, implying that they consume unnecessary observations. In the first part, we study three conservativeness sources in fully sequential indifference-zone (IZ) procedures and use experiments to quantify the impact of each source in terms of the number of observations, followed by an asymptotic analysis on the impact of the critical one. Then we propose new asymptotically valid procedures that lessen the critical conservativeness source, by mean update with or without variance update. Experimental results showed that new procedures achieved meaningful improvement on the efficiency. The second part is developing 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 nonoverlapping 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, WDFTCa computes a similar Hotelling’s 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 nonnormal test processes revealed that WDFTCa outperformed existing nonadaptive profile-monitoring schemes.
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