Monitoring the Process Mean of Autocorrelated Data

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.

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

2008

Author dc:creator

• King, Jesse Dorian

Contributors dc:contributor

• B. Oluyede
• P. Humphrey

• ETD
• ARMA
• ARIMA
• Autocorrelation
• Shewhart
• CUSUM
• Control charts
• Gapping
• Simulation
• Autocorrection (Statistics)

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/648

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-1648