Title page for ETD etd-11102005-141105


Type of Document Dissertation
Author Lu, Chao-Wen
URN etd-11102005-141105
Title Control charts based on residuals for monitoring processes with correlated observations
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Reynolds, Marion R. Jr. Committee Chair
Arnold, Jesse C. Committee Member
Foutz, Robert V. Committee Member
Lentner, Marvin M. Committee Member
Ye, Keying Committee Member
Keywords
  • Quality control charts
  • diagrams
Date of Defense 1993-08-05
Availability restricted
Abstract

In statistical process control, it is usually assumed that observations on the process output at different times are lID. However, for many processes the observations are correlated and control charts for monitoring these processes have recently received much attention. For monitoring the process level, this study evaluates the properties of control charts, such as the EWMA chart and the CUSUM chart, based on the residuals from the forecast values of an ARMA model. It is assumed that the process mean is a ftrst order autoregressive (AR(l)) model and the observations are the mean plus a random error. Properties of these charts are evaluated using a Markov chain approach or an integral equation approach. The performance of control charts based on the residuals is compared to the performance of control charts based on the original observations. A combined chart using forecasts and residuals as the control statistics as well as a combined chart using the EWMA of observations and the EWMA of residuals as the control statistics are also studied by simulation. It is found that no universally "good" chart exists among all the charts investigated in this study.

In addition, for monitoring the process variance, two kinds of EWMA chart based on residuals are studied and compared.

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