{"id":{"repo_id":"gsu","oai_identifier":"oai:digitalcommons.georgiasouthern.edu:etd-1648"},"canonical_url":"https://search.dev.ndltd.org/etd/gsu/oai:digitalcommons.georgiasouthern.edu:etd-1648","repository":{"repo_id":"gsu","name":"Georgia Southern University","base_url":"https://digitalcommons.georgiasouthern.edu/do/oai/"},"display":{"title":"Monitoring the Process Mean of Autocorrelated Data","abstract":"When modeling the stochastic behavior of a sequence { } t X of the quality measurement X on the output of a production process, it is usually assumed the measurements taken over time are independent and identically distributed. Multiple authors have pointed out that significant autocorrelation can affect the performance of traditional control charting procedures. One family of models for time series data are the autoregressive integrated moving average (ARIMA) models. These models are well suited to model production processes, in which the observations are autocorrelated. It is our interest to examine these models. Meaning is given to the process being in-control and out-of-control in terms of the parameters of the model. The performance of the Shewhart X chart and CUSUM X chart are compared. This includes determining the number of unobserved values between samples for the charts to perform as they would be expected if the samples were independent. Some recommendations are given.","abstract_html":"When modeling the stochastic behavior of a sequence { } t X of the quality measurement X on the output of a production process, it is usually assumed the measurements taken over time are independent and identically distributed. Multiple authors have pointed out that significant autocorrelation can affect the performance of traditional control charting procedures. One family of models for time series data are the autoregressive integrated moving average (ARIMA) models. These models are well suited to model production processes, in which the observations are autocorrelated. It is our interest to examine these models. Meaning is given to the process being in-control and out-of-control in terms of the parameters of the model. The performance of the Shewhart X chart and CUSUM X chart are compared. This includes determining the number of unobserved values between samples for the charts to perform as they would be expected if the samples were independent. Some recommendations are given.","abstract_has_math":false,"creators":["King, Jesse Dorian"],"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":["B. Oluyede","P. Humphrey"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-05-01T07:00:00Z","date_published":"2008-05-01T07:00:00Z","updated_at":"2026-07-24T02:27:19Z","subjects":["ETD","ARMA","ARIMA","Autocorrelation","Shewhart","CUSUM","Control charts","Gapping","Simulation","Autocorrection (Statistics)"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/648","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["B. Oluyede","P. 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Multiple authors have pointed out that significant autocorrelation can affect the performance of traditional control charting procedures. One family of models for time series data are the autoregressive integrated moving average (ARIMA) models. These models are well suited to model production processes, in which the observations are autocorrelated. It is our interest to examine these models. Meaning is given to the process being in-control and out-of-control in terms of the parameters of the model. The performance of the Shewhart X chart and CUSUM X chart are compared. This includes determining the number of unobserved values between samples for the charts to perform as they would be expected if the samples were independent. Some recommendations are given."]},{"key":"dc:title","label":"Title","values":["Monitoring the Process Mean of Autocorrelated Data"]}]}],"canonical_facts":{"dc:contributor":["B. Oluyede","P. Humphrey"],"dc:creator":["King, Jesse Dorian"],"dc:date.available":["2013-10-17T07:00:00Z"],"dc:description.abstract":["When modeling the stochastic behavior of a sequence { } t X of the quality measurement X on the output of a production process, it is usually assumed the measurements taken over time are independent and identically distributed. Multiple authors have pointed out that significant autocorrelation can affect the performance of traditional control charting procedures. One family of models for time series data are the autoregressive integrated moving average (ARIMA) models. These models are well suited to model production processes, in which the observations are autocorrelated. It is our interest to examine these models. Meaning is given to the process being in-control and out-of-control in terms of the parameters of the model. The performance of the Shewhart X chart and CUSUM X chart are compared. This includes determining the number of unobserved values between samples for the charts to perform as they would be expected if the samples were independent. Some recommendations are given."],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/648"],"dc:subject":["ETD","ARMA","ARIMA","Autocorrelation","Shewhart","CUSUM","Control charts","Gapping","Simulation","Autocorrection (Statistics)"],"dc:title":["Monitoring the Process Mean of Autocorrelated Data"],"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"}