Term of Award

Spring 2008

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Charles Champ

Committee Member 1

B. Oluyede

Committee Member 2

P. Humphrey

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.

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