Distribution-free statistical process control and Bayesian feasibility determination

This thesis consists of three main 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. The main idea is to convert each observation vector into a one-dimensional $T^2$ quantity that captures cross-correlation. The $T^2$ quantities form a univariate auto-correlated process, and CUSUM statistics are constructed on the $T^2$ quantities. Then using the fact that the CUSUM statistics on the auto-correlated process behave as a reflected Brownian motion asymptotically under some conditions, the control limits of the CUSUM procedure are analytically determined by setting the first-passage time of the Brownian motion equal to a target in-control average run length. We compare the performance of our procedure with three baseline procedures on simulated data with various cross- and auto-correlation 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 for a manufacturing process 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. Existing image-based monitoring procedures usually assume each component in a monitored image process has normally distributed observations, and the observations are independent or following a specific correlation structure. However, a real-world case such as a battery coating process often violates these assumptions. We propose a distribution-free image monitoring procedure to detect a shift in the mean matrix of monitored images. 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 Chapter 2. The effectiveness of the proposed procedure, measured by average run lengths, is demonstrated using various simulated data and a real-data example from a battery coating process. In Chapter 4, we consider the problem of finding a set of feasible inputs in the presence of constraints on multiple performance measures when the constraints are stochastic in that the performance measures can only be evaluated via noisy observations. When similar inputs are more likely to have similar performance measures and when each observation is expensive, a Gaussian process (GP) can be employed to model the performance measures. One previous work utilizes a GP for feasibility determination with a single stochastic constraint. We extend this previous work to multiple constraints. The decision on which input to test next to obtain a new observation is based on a value-of-information function but the calculation of the function can take long, hindering the efficient implementation of the Bayesian feasibility check procedure. To accelerate the computation of the proposed Bayesian procedure, we propose another version with an approximation for the value-of-information function that is quick and easy to calculate. We prove the convergence of our proposed procedures and demonstrate the effectiveness of the procedures incorporating both independent and multi-task GPs.

Date

2022-08-26

Resource Type

Text

Resource Subtype

Dissertation

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