Multivariate Monitoring of the Process Mean Vector with Sequential Sampling

Abstract

Multivariate control charts are used to monitor a process when more than one quality variable associated with the process is being observed. The standard practice when using any control chart to monitor a process is to take samples of fixed size at regular sampling intervals. Here we investigate multivariate exponentially weighted moving average (MEWMA) control charts based on sequential sampling. When sequential sampling is used, observations at a sampling point are taken in groups of one or more observations, and the number of groups actually taken is a random variable that depends on the data. The basic idea is that sampling starts with a small initial group of observations, and no additional sampling is done at this point if there is no indication of a problem with the process. If there is some indication of a problem with the process, then an additional group or groups of observations is taken at this sampling point. A signal is given after any group if there is a strong indication of a problem with the process. The performance of the MEWMA control chart based on sequential sampling is compared with the performance of standard control charts. It is shown that the MEWMA chart based on sequential sampling is much more efficient in detecting changes in the process mean vector than standard control charts based on nonsequential sampling. Sequential sampling performs best when there is the possibility of many groups at each sampling point, but sequential sampling is still substantially better than nonsequential sampling when only two groups are allowed.