T Square Partitioned

If you are monitoring a large number of correlated process characteristics, you can use the T Square Partitioned option to construct a control chart based on principal components. If a small number of principal components explains a large portion of the variation in your measurements, then a multivariate control chart based on these big components might be more sensitive than a chart based on your original, higher-dimensional data.

The T Square Partitioned option is also useful when your covariance matrix is ill-conditioned. When this is the case, components with small eigenvalues, explaining very little variation, can have a large, and misleading, impact on T2. It is useful to separate out these less important components when studying process behavior.

Once you select the T Square Partitioned option, you need to decide how many major principal components to use.

The option creates two multivariate control charts: T Square with Big Principal Components and T Square with Small Principal Components. Suppose that you enter r as the number of major components when you first select the option. The chart with Big Principal Components is based on the r principal components corresponding to the r largest eigenvalues. These are the r components that explain the largest amount of variation, as shown in the Percent and Cum Percent columns in the Principal Components: on Covariances reports. The chart with Small Principal Components is based on the remaining principal components.

For a given subgroup, its T2 value in the Big Principal Components chart and its T2 value in the Small Principal Components chart sum to its overall T2 statistic presented in the T2 with All Principal Components report. For more information about how the partitioned T2 values are calculated, see Kourti, T. and MacGregor, J. F. (1996).