College of Graduate Studies: Theses & Dissertations

Term of Award

Spring 2026

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Arpita Chatterjee

Committee Member 1

Ionut E. Iacob

Committee Member 2

Ahmed Al-Taweel

Abstract

In many industries, it is important to assess whether a machine or system is operating within acceptable limits or has gone out of control. This project applies Bayesian statistics to monitor a process over time and detect changes in its behavior. First, initial data are collected to understand the system’s typical performance and to form a starting prior distribution. As new observations arrive over time, the prior is updated through Bayesian inference, combining past information with incoming data. This iterative updating creates a continuous monitoring framework that adapts as more evidence becomes available. When the updated results suggest that the system is no longer behaving as expected, the process is flagged as out of control. The procedure follows a cycle of data collection, belief updating, and control assessment, without requiring strict distributional assumptions. The main objective is to study out-of-control performance under different shift scenarios in the underlying distribution.

Research Data and Supplementary Material

No

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