Title page for ETD etd-03012006-103618


Type of Document Dissertation
Author Zhong, Xin
URN etd-03012006-103618
Title Efficient Sampling Plans for Control Charts When Monitoring an Autocorrelated Process
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Reynolds, Marion R. Jr. Committee Chair
Birch, Jeffrey B. Committee Member
Vining, G. Geoffrey Committee Member
Woodall, William H. Committee Member
Keywords
  • dispersed sampling
  • concentrated sampling
  • autocorrelation
  • Shewhart control chart
  • statistical process control
  • exponentially weighted moving average control char
Date of Defense 2006-02-24
Availability unrestricted
Abstract
This dissertation investigates the effects of autocorrelation on the performances of various sampling plans for control charts in detecting special causes that may produce sustained or transient shifts in the process mean and/or variance. Observations from the process are modeled as a first-order autoregressive process plus a random error. Combinations of two Shewhart control charts and combinations of two exponentially weighted moving average (EWMA) control charts based on both the original observations and on the process residuals are considered. Three types of sampling plans are investigated: samples of n = 1, samples of n > 1 observations taken together at one sampling point, or samples of n > 1 observations taken at different times. In comparing these sampling plans it is assumed that the sampling rate in terms of the number of observations per unit time is fixed, so taking samples of n = 1 allows more frequent plotting. The best overall performance of sampling plans for control charts in detecting both sustained and transient shifts in the process is obtained by taking samples of n = 1 and using an EWMA chart combination with a observations chart for mean and a residuals chart for variance. The Shewhart chart combination with the best overall performance, though inferior to the EWMA chart combination, is based on samples of n > 1 taken at different times and with a observations chart for mean and a residuals chart for variance.
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