{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1663"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1663","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"Monitoring for a Shift in a Process Covariance Matrix Using the Generalized Variance","abstract":"The commonly recommended charts for monitoring the mean vector are affected by a shift in the covariance matrix. As in the univariate case, a chart for monitoring for a change in the covariance matrix should be examined first before examining the chart used to monitor for a change in the mean vector. One such chart is the one that plots the generalized sample variance lSl verses the sample number t. We propose to study charts based on the statistics V = l(n - 1) Σ₀-¹ Sl¹/̳p̳ and U = 1n (l (n-1) Σ₀-¹Sl¹/̳p̳), where n is the sample size and Σ₀ is the in-control value of the process covariance matrix Σ. In particular, we will study the Shewhart V and U charts supplemented with runs rules. Also, we examine the methods that are useful in studying the run length properties of the cumulative sum (CUSUM) U charts. Further, we will study the effect that estimating Σ₀ has on the performance of these charts. Guidance will be given for designing the Shewhart charts with runs rules with illustrative examples.","abstract_html":"The commonly recommended charts for monitoring the mean vector are affected by a shift in the covariance matrix. As in the univariate case, a chart for monitoring for a change in the covariance matrix should be examined first before examining the chart used to monitor for a change in the mean vector. One such chart is the one that plots the generalized sample variance lSl verses the sample number t. We propose to study charts based on the statistics V = l(n - 1) Σ₀-¹ Sl¹/̳p̳ and U = 1n (l (n-1) Σ₀-¹Sl¹/̳p̳), where n is the sample size and Σ₀ is the in-control value of the process covariance matrix Σ. In particular, we will study the Shewhart V and U charts supplemented with runs rules. Also, we examine the methods that are useful in studying the run length properties of the cumulative sum (CUSUM) U charts. Further, we will study the effect that estimating Σ₀ has on the performance of these charts. Guidance will be given for designing the Shewhart charts with runs rules with illustrative examples.","abstract_has_math":false,"creators":["Parham, Kellen M."],"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","Patricia Humphrey"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-05-01T07:00:00Z","date_published":"2010-05-01T07:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","Average run length","Cumulative sum charts","Independent samples","Integral equations","Markov chain","Multivariate normal distribution","Shewhart charts","Mathematical statistics","Graphic methods"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/663","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Broderick O. 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As in the univariate case, a chart for monitoring for a change in the covariance matrix should be examined first before examining the chart used to monitor for a change in the mean vector. One such chart is the one that plots the generalized sample variance lSl verses the sample number t. We propose to study charts based on the statistics V = l(n - 1) Σ₀-¹ Sl¹/̳p̳ and U = 1n (l (n-1) Σ₀-¹Sl¹/̳p̳), where n is the sample size and Σ₀ is the in-control value of the process covariance matrix Σ. In particular, we will study the Shewhart V and U charts supplemented with runs rules. Also, we examine the methods that are useful in studying the run length properties of the cumulative sum (CUSUM) U charts. Further, we will study the effect that estimating Σ₀ has on the performance of these charts. Guidance will be given for designing the Shewhart charts with runs rules with illustrative examples."]},{"key":"dc:title","label":"Title","values":["Monitoring for a Shift in a Process Covariance Matrix Using the Generalized Variance"]}]}],"canonical_facts":{"dc:contributor":["Broderick O. Oluyede","Patricia Humphrey"],"dc:creator":["Parham, Kellen M."],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["The commonly recommended charts for monitoring the mean vector are affected by a shift in the covariance matrix. As in the univariate case, a chart for monitoring for a change in the covariance matrix should be examined first before examining the chart used to monitor for a change in the mean vector. One such chart is the one that plots the generalized sample variance lSl verses the sample number t. We propose to study charts based on the statistics V = l(n - 1) Σ₀-¹ Sl¹/̳p̳ and U = 1n (l (n-1) Σ₀-¹Sl¹/̳p̳), where n is the sample size and Σ₀ is the in-control value of the process covariance matrix Σ. In particular, we will study the Shewhart V and U charts supplemented with runs rules. Also, we examine the methods that are useful in studying the run length properties of the cumulative sum (CUSUM) U charts. Further, we will study the effect that estimating Σ₀ has on the performance of these charts. Guidance will be given for designing the Shewhart charts with runs rules with illustrative examples."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/663"],"dc:subject":["ETD","Average run length","Cumulative sum charts","Independent samples","Integral equations","Markov chain","Multivariate normal distribution","Shewhart charts","Mathematical statistics","Graphic methods"],"dc:title":["Monitoring for a Shift in a Process Covariance Matrix Using the Generalized Variance"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:19Z"}