A change point method for linear profile data

We propose a change point approach based on the segmented regression technique for testing the constancy of the regression parameters in a linear profile data set. Each sample collected over time in the historical data set consists of several bivariate observations for which a simple linear regression model is appropriate. The change point approach is based on the likelihood ratio test for a change in one or more regression parameters. We compare the performance of this method to that of the most effective Phase I linear profile control chart approaches using a simulation study. The advantages of the change point method over the existing methods are greatly improved detection of sustained step changes in the process parameters and improved diagnostic tools to determine the sources of profile variation and the location(s) of the change point(s). Also, we give an approximation for appropriate thresholds for the test statistic. The use of the change point method is demonstrated using a data set from a calibration application at the National Aeronautics and Space Administration (NASA) Langley Research Center.