Shows the T2 chart. Hotelling’s T2 chart is a multivariate extension of the X-bar chart that takes correlation into account.
Constructs multivariate control charts based on the principal components of Y. Specify the number of major principal components for T2. See T Square Partitioned.
Set the α level used to calculate the control limit. The default is α=0.05.
Creates a new column in the data table. Stores a formula in the column that calculates the T2 values.
Creates a new data table containing target statistics for the process. Target statistics include: sample size, the number of samples, mean, standard deviation, and any correlations.
(Not available for sub-grouped data) Shows a Change Point Detection plot of test statistics by row number and indicates the row number where the change point appears. See Change Point Detection.
Shows reports showing eigenvalues and their corresponding eigenvectors. Principal components help you understand which of the many variables you might be monitoring are primarily responsible for the variation in your process. See Principal Components.
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 details about how the partitioned T2 values are calculated, see Kourti, T. and MacGregor, J. F., 1996.
When the data set consists of multivariate individual observations, a control chart can be developed to detect a shift in the mean vector, the covariance matrix, or both. This method partitions the data and calculates likelihood ratio statistics for a shift. These statistics are divided by the expected value for no shift and are then plotted by the row number. A Change Point Detection plot readily shows the change point for a shift occurring at the maximized value of the test statistic.
Note: The Change Point Detection method is designed to show a single shift in the data. Detect multiple shifts by recursive application of this method.
Provides a test of whether the correlation remaining in the data is of a random nature. This is a Bartlett test of sphericity. When this test rejects the null hypothesis, this implies that there is structure remaining in the data that is associated with this eigenvalue.
p-value for the test.
Table of eigenvectors corresponding to the eigenvalues. Note that each eigenvector is divided by the square root of its corresponding eigenvalue.
For more information about principal components, see the Multivariate Methods book.