Multivariate process control for detection and cause identification of location shifts

Most processes involve more than one process/product output variable, multiple process input/regulatory variables, and a category of noise variables, which consists of factors not considered in the model, or those external to the process. Since output variables are not necessarily independent of each other, an adequate approach involves multivariate process control for monitoring of the process. It is of practical value to determine possible causes in the event of a change in the process location, which is detected through a multivariate control chart. In this paper, for cause identification, one of the methods uses information from only the process input variables, while the other uses a generalised measure, based on the residuals, that incorporates the process input and output variables. A simulation approach is adopted to investigate the performance of the proposed estimators as well as the traditional estimator that incorporates only the process/product output variables. Based on a selected performance measure of the average run length of the time to first detection, when the location parameter has changed, the proposed methods perform favourably compared to the traditional estimator.