Multivariate Shewhart X-bar Chart
by Saeed Golnabi and Ali Houshmand
In univariate quality control, the X-bar Charts have been
useful in determining whether the process mean is in-control or not. It
would be very useful to have a similar chart applied to the
multivariate case. The existing methods do not provide all the
information that a quality control practitioner would like to possess
such as the indication of which variables are causing the process to be
out-of-control. In this paper, we propose a method which allows us to
simultaneously control the overall process quality characteristics and
to identify the responsible variables leading to an out-of-control
condition. This method is based on the adequate selection of the
symmetric square root of the correlation matrix. The associated
critical region is also discussed. The process considered is assumed to
be multivariate normal with parameters known from historical data or
estimated from a large sample. We call this method, "Multivariate
Shewhart Chart (MS Chart)", because it reduces to the Shewhart Chart
when the process involves only one variable. The procedure has been
illustrated with the help of three examples, two of which have been
frequently used by other authors, and one simulated.
Multivariate Quality Control, Multivariate Shewhart Chart,
Symmetric Square Root, Critical Region
Rachel T. Fouladi,
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