Analysis and Design of One- and Two-Sided Cusum Charts with Known and Estimated Parameters

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.

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2007

Author dc:creator

• Dunbar, Martin Xavier

Contributors dc:contributor

• Broderick O. Oluyede
• Hani Samawi

• ETD
• ARL
• CUSUM
• Integral equations
• Markov chain
• Run length
• Mathematical statistics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/651

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1651