Dr. Seong-Hee Kim

Dr. Xiaoming Huo, Dr. Jianjun Shi, Dr. James R. Wilson (North Carolina

State University), and Dr. Youngmi Hur (Yonsei University)

Thursday, February 26 2015, 9:30AM

Academic Office - Groseclose 204

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, Hotellingâ€™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 Hotellingâ€™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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