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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Khamitova, Anna"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Broderick O. Oluyede","Daniel Linder"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:28:00Z","subjects":["ETD","Chi Square distribution","covariance matrix","integral equation","Markov chain","Meijer G function","simulation","Statistical Methodology","Statistical Models"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1142","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Broderick O. Oluyede","Daniel Linder"]},{"key":"dc:creator","label":"Author","values":["Khamitova, Anna"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-07-06T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Chi Square distribution","covariance matrix","integral equation","Markov chain","Meijer G function","simulation","Statistical Methodology","Statistical Models"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1142"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Exponentially Weighted Moving Average Charts for Monitoring the Process Generalized Variance"]}]}],"canonical_facts":{"dc:contributor":["Broderick O. Oluyede","Daniel Linder"],"dc:creator":["Khamitova, Anna"],"dc:date.available":["2014-07-06T07:00:00Z"],"dc:description.abstract":["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.
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