Term of Award
Summer 2020
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (restricted to Georgia Southern)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Department of Mathematical Sciences
Committee Chair
Charles Champ
Committee Member 1
Kyle Bradford
Committee Member 2
Divine Wanduku
Abstract
A control chart is used as an aid to a practitioner in bringing a production process into a state of statistical in control. In this phase (Phase I), a control chart is also used as an aid in defining what is meant by the process being in a state of statistical in control. Once a process has been brought into a state of statistical in control, a control chart is used to monitor for a change in a quality characteristic of the process. A control chart is used in the monitoring phase (Phase II) to signal a potential out-of-control process if there is strong evidence the process is no longer in-control. We will assume that if the chart signals, the process is out-of-control. Our interest is to find the last sampling time the process was in control. This time is known as the change point. The method we will use is referred to as the maximum likelihood method. We show that likelihood function method in the parameters estimated case is equivalent to the parameters known case requiring the in-control process parameters. We propose a new change point method that does not require the in-control process parameters. We prove that the methods used with cumulative sum (CUSUM) chart for monitoring the process mean both when the in-control parameters are known and when they are estimated are the same methods used with the Shewhart chart. Further, we derived the maximum likelihood change point method for the Hotelling’s T2 chart both when the process in-control parameters are known and when they are estimated. As in the univariate case, the parameters estimated case uses the same method as the parameters known case. We propose a new change point method that does not depend on knowing the in-control process parameters.
Recommended Citation
Alliu, Ibrahim L., "Change Point Analysis with Control Charts" (2020). Electronic Theses and Dissertations. 2127.
https://digitalcommons.georgiasouthern.edu/etd/2127
Research Data and Supplementary Material
No
