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Activity Number:
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343
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Type:
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Contributed
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Date/Time:
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Tuesday, July 31, 2007 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Quality and Productivity
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| Abstract - #308167 |
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Title:
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Monitoring Variation in a Multivariate Process with Sample Size Smaller Than the Dimension
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Author(s):
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John Young*+ and Robert L. Mason and Youn-Min Chou
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Companies:
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McNeese State University and Southwest Research Institute and University of Texas at San Antonio
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Address:
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1750 Bilbo St, Lake Charles, LA, 70601,
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Keywords:
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MVSPC ; Covariance Matrix
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Abstract:
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A number of procedures have recently been developed for monitoring changes in the covariance matrix of a multivariate normal process. All of the methodologies that are based on the generalized sample variance require that the sample size, n, be greater than the number of process variables, p, i.e., n > p. We introduce a procedure for monitoring changes in the variation of the covariance matrix for a MV normal process based on samples of size n > 1 with no restrictions relative to p. We use a control statistic that is a function of the ratio of the determinants of two separate estimates of the covariance matrix, and the distribution of this statistic is based on the distribution of Wilks' likelihood ratio criterion. The proposed statistic is shown to be insensitive to some of the inherent weaknesses associated with using a statistic based on only the generalized variance of a sample.
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