*Title:*
Statistical Selection and Wavelet-Based Profile Monitoring

*Advisors: *
Dr. Seong-Hee Kim

*Committee:*
Dr. Xiaoming Huo, Dr. Jianjun Shi, Dr. James R. Wilson (North Carolina
State University), and Dr. Youngmi Hur (Yonsei University)

*Date and time:*
Thursday, February 26 2015, 9:30AM

*Location:  *
Academic Office - Groseclose 204

*Abstract:*

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.