Complete the following steps to interpret a T^{2}-Generalized Variance chart. Key output includes the T^{2} chart, the Generalized Variance chart, and test results.

The generalized variance chart plots the joint process variability of several related variables. The center line is the determinant of the sample covariance matrix. The lower and upper control limits are based on the number of variables and number of observations in each subgroup.

The Generalized Variance chart should be in control before you interpret the Tsquared chart. When the Generalized Variance chart is out of control, the control limits on the Tsquared chart will not be accurate and may falsely indicate an out-of-control condition.

Red points indicate subgroups that are above the upper control limit and not in control. One disadvantage to multivariate charts is that the scale is unrelated to the scale of any of the variables, and out-of-control signals do not reveal which variable (or combination of variables) caused the signal.

The T^{2} chart plots the T^{2} for each subgroup to measure whether the process locations of several related variables are simultaneously in control. The center line is the median of the theoretical distribution of T^{2} statistics. The upper control limit is based on the number of samples, the size of each sample, and the number of variables.

Minitab identifies points that are outside the control limit with a red symbol. Out-of-control points may indicate the presence of special causes. One disadvantage to multivariate charts is that the scale is unrelated to the scale of any of the variables, and out-of-control signals do not reveal which variable (or combination of variables) caused the signal.

Investigate any points that are above the upper control limit. The Session window output shows exactly which points are above the control limit, as shown here.

Test Results for T² Chart of Stay, Satisfaction
Point Variable P-Value
Greater Than UCL 2 Stay 0.0030
Satisfaction 0.0067
18 Stay 0.0010
Satisfaction 0.0002
19 Satisfaction 0.0000
* WARNING * If graph is updated with new data, the results above may no longer
be correct.