PhD Defense by Di Liu
Dear faculty members and fellow students,
You are cordially invited to attend my thesis defense.
Thesis Title: Distribution-Free Statistical Process Control and Bayesian Feasibility Determination
Dr. Seong-Hee Kim, School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Yao Xie, School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Nagi Gebraeel, School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Thomas Kurfess, School of Mechanical Engineering, Georgia Institute of Technology
Dr. Kamran Paynabar, School of Industrial and Systems Engineering, Georgia Institute of Technology
Date and Time: Tuesday, August 16th, 2022, 10:00 am (EDT)
Meeting Link: https://gatech.zoom.us/j/97078829363
This thesis consists of three parts. The first two parts focus on multivariate time-series monitoring that commonly arises in the quality control problems, and the third part considers the feasibility determination via simulation which has a broad range of applications including manufacturing process control.
In Chapter 2, we consider the problem of detecting a shift in the mean of a multivariate time-series process with a general marginal distribution and a general cross- and auto-correlation structure. We propose a distribution-free monitoring procedure that does not need model fitting nor trial-and-error calibration. Control limit of the procedure can be determined analytically, which allows efficient implementation and easy generalization. We compare the performance of our procedure with three baseline procedures on simulated data with various settings and real data from a wafer etching process. The proposed procedure delivers actual in-control average run length close to the target and shows comparable or better performance in detecting a shift in mean compared to baseline procedures.
In Chapter 3, we consider an image monitoring problem where a series of 2-dimensional images are converted into a series of random matrices and the mean of these random matrices is expected to be a matrix with rank one. We propose a distribution-free image monitoring procedure to detect a shift in the mean matrix. Two monitoring statistics are calculated based on the singular value decomposition technique, and the two statistics are composited into a two-variate vector. Then the two-variate vectors are monitored by the procedure introduced in the previous chapter. The effectiveness of the proposed procedure is demonstrated using various simulated data and a real-data example from a battery coating process.
In Chapter 4, we consider the problem of identifying candidate inputs with performance measures satisfying specific constraints which can only be evaluated via stochastic simulation. When similar inputs are more likely to have similar performance measures, Gaussian processes (GP) are suitable for modeling the mean performances. We propose a Bayesian procedure utilizing GP for feasibility determination with multiple constraints. The procedure makes sampling decisions sequentially based on a value-of-information (VOI) function. We analyze the theoretical guarantee of its performance, and provide an approximation of the VOI function to accelerate computation. Numerical experiments are conducted to demonstrate the effectiveness of the procedure and compare the performance of incorporating independent GPs and multi-task GP in the procedure.