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A new control chart in contaminated data of t ‐Student distribution for individual observations
Author(s) -
Alfaro José Luis,
Ortega Juan Fco.
Publication year - 2012
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.946
Subject(s) - control chart , outlier , normality , computer science , chart , \bar x and r chart , statistics , normal distribution , statistical process control , shewhart individuals control chart , x bar chart , multivariate normal distribution , student's t distribution , control limits , data mining , ewma chart , econometrics , multivariate statistics , mathematics , process (computing) , operating system , volatility (finance) , autoregressive conditional heteroskedasticity
Control charts are the most popular tool for monitoring production quality. In traditional control charts, it is usually supposed that the observations follow a multivariate normal distribution. Nevertheless, there are many practical applications where the normality assumption is not fulfilled. Furthermore, the performance of these charts in the presence of measurement errors (outliers) in the historical data has been improved using robust control charts when the observations follow a normal distribution. In this paper, we develop a new control chart for t ‐Student data based on the trimmed T 2 control chart ( T R 2 ) through the adaptation of the elements of this chart to the case of this distribution. Simulation studies show that a T R 2 control chart performs better than T 2 in t ‐Student samples for individual observations. Copyright © 2012 John Wiley & Sons, Ltd.