Exponentially Weighted Moving Average Charts for Monitoring the Process Generalized Variance

<p>The exponentially weighted moving average chart based on the sample generalized variance is studied under the independent multivariate normal model for the vector of quality measurements. The performance of the chart is based on an analysis of the chart's initial and steady-state run length distributions. The three methods that are commonly used to determinate run length distribution, simulation, the integral equation method, and the Markov chain approximation are discussed. The integral equation and Markov chain approaches are analytical methods that require a nu- merical method for determining the probability density and cumulative distribution functions describing the distribution of the sample generalized variance. Two meth- ods for determining numerically these functions are discussed. The equivalence of the integral equation and Markov chain methods is shown resulting in a new method for obtaining a Markov chain approximation of the chart. Some examples of the implementation of these methods are given using MATLAB.</p>

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

2014

Author dc:creator

• Khamitova, Anna

Contributors dc:contributor

• Broderick O. Oluyede
• Daniel Linder

• ETD
• Chi Square distribution
• covariance matrix
• integral equation
• Markov chain
• Meijer G function
• simulation
• Statistical Methodology
• Statistical Models

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1142

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2200