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Properties of Multivariate Control Charts with Estimated Parameters
by
Charles W. Champ
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460-8093
Coauthors: Dr. L. Allison Jones-Farmer, Management Department, Auburn University, Auburn, AL 36849-5247
The Hotelling's Tē, multivariate exponentially weighted moving average (MEWMA), and several multivariate cumulative sum (MCUSUM) charts are examined in this paper. Two descriptions are given of each chart with estimated parameters for monitoring the mean of a vector of quality measurements. For each chart, one description explains how the chart can be applied with estimated parameters in practice and the other description is useful for analyzing the run length performance of the chart. It is shown that, if the covariance matrix is in control, the run length distribution of most of these charts depends only on the distributional parameters through the statistical size of the shift. Simulation is used to provide performance analyses and comparisons of these charts. An example is given to illustrate the MCUSUM and MEWMA charts when parameters are estimated.
Date received: July 21, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqt-32.