Classical T-Square Charts |
Classical charts are defined as follows. Assume that there are
observations for
variables, denoted by
, where
is a
-dimensional vector. The
statistic for observation
is
![]() |
where
![]() |
and
![]() |
For purposes of deriving control limits for the chart, it is assumed that
has a
-dimensional multivariate normal distribution with mean vector
and covariance matrix
for
. The classical formulation of the
chart does not involve a principal components model for the data and bases the computation of the
on the sample covariance matrix
. Refer to Alt (1985) for theoretical details and to the section Multivariate Control Charts for an example.
A classical chart is equivalent to a
chart based on a full principal components model (with
components) as discussed in the section Relationship of Principal Components to Multivariate Control Charts. See Example 10.2 for more discussion.
Note: This procedure is experimental.