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 test statistics for a shift. The statistic that is plotted on the control chart is an observation’s likelihood ratio test statistic divided by the product of the following:
• Its approximate expected value assuming no shift.
• An approximate value for an upper control limit.
Division by the approximate upper control limit allows the points to be plotted against an effective upper control limit of 1. A Change Point Detection plot readily shows the change point for a shift occurring at the maximized value of the control chart statistic. The Change Point Detection implementation in JMP is based on Sullivan and Woodall (2000) and is described in Statistical Details for Change Point Detection.
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.
Note the following about the Change Point Detection plot:
• Values above 1.0 indicate a possible shift in the data.
• Control chart statistics for the Change Point Detection plot are obtained by dividing the likelihood ratio statistic of interest (either a mean vector or a covariance matrix) by a normalizing factor.
• The change point of the data occurs for the observation having the maximum test statistic value for the Change Point Detection plot.
Note the following about the scatterplot matrix:
• This plot shows the shift in the sample mean vector.
• In the Example of Change Point Detection, data are divided into two groups. The first 24 observations are classified as the first group. The remaining observations are classified as the second group.