Classical charts are defined as follows. Assume that there are n observations for p variables, denoted by , where is a pdimensional vector. The statistic for observation i is

where

and

For purposes of deriving control limits for the chart, it is assumed that has a pdimensional multivariate normal distribution with mean vector and covariance matrix for . The classical formulation of the chart does not involve a principal component model for the data, and it bases the computation of on the sample covariance matrix . See Alt (1985) for theoretical details and the section Multivariate Control Charts for an example.
A classical chart is equivalent to a chart based on a full principal component model (with p components), as discussed in the section Relationship of Principal Components to Multivariate Control Charts. See Example 12.2 for more information.