Term of Award

Spring 2007

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 of Mathematical Sciences

Committee Chair

Charles W. Charles

Committee Member 1

Broderick O. Oluyede

Committee Member 2

Hani Samawi


The integral equation and Markov chain methods for analyzing the performances of one- and two-sided CUSUM X charts with known and estimated in-control process parameters are studied. Some new integral equations for analyzing the two-sided CUSUM X are derived. These methods provide us with ways to approximate the run length distribution of the chart. Since parameters of the run length distribution are commonly used measures of the performance of a control chart, it is important to choose an accurate approximation method. We develop some new Markov chain approximations using methods similar to the methods for approximating a solution to integral equations that describe the run length distribution.

Research Data and Supplementary Material