A Comparison of Multivariate Control Charts for Individual Observations
作者:
SullivanJoe H.,
WoodallWilliam H.,
期刊:
Journal of Quality Technology
(Taylor Available online 1996)
卷期:
Volume 28,
issue 4
页码: 398-408
ISSN:0022-4065
年代: 1996
DOI:10.1080/00224065.1996.11979698
出版商: Taylor&Francis
关键词: Hotelling's T2 Statistic;Multivariate Control Charts;Outliers;Statistical Process Control
数据来源: Taylor
摘要:
For multivariate statistical process control with individual observations the usually recommended procedure in the retrospective phase is the Hotelling'sT2control chart. All the observations are pooled to estimate the mean vector and covariance matrix. An out-of-control signal results if theT2value of any observation exceeds an upper control limit. We show this procedure isnoteffective in detecting a shift in the mean vector because the covariance matrix is badly estimated. Somewhat surprisingly, the signal probability decreases with increasingly severe shifts in the mean vector. We compare several alternative methods for estimating the covariance matrix and recommend a procedure analogous to the use of moving ranges in the univariate case. This procedure uses the vector differences between successive observations to estimate the in-control covariance matrix of the process. With this more robust estimate, step and ramp shifts in the mean vector are more likely to be detected in the retrospective phase.
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