A study of multivariate pre-control charts

The quality of the output of a production process is often measured by the joint level of several correlated characteristics. Through multivariate control charts, one will be able to detect a process change and prevent defects from occurring by identifying and eliminating assignable causes of variation. In contrast to the traditional control charts, pre-control charts focus on evaluating the process capability during the set-up stage and detecting the process change during the mass production stage. However, the set-up and monitoring rules as well as the sample size for multivariate pre-control charts have not been thoroughly studied (to our knowledge). The main purpose of this research is to develop these rules and compare the performances of detecting a process change using multivariate pre-control charts versus Hotelling T2 control charts when the quality characteristics follow a multivariate normal distribution. These objectives can be achieved by two statistical measures known as the in-control and out-of-control average run lengths (ARLs). The simulation results and a numerical example further demonstrate the usefulness of the new set-up and monitoring rules we proposed for multivariate pre-control charts.