Multivariate Cuscore control charts for monitoring the mean vector in autocorrelated processes

In many systems, quantitative observations of process variables can be used to characterize a process for quality control purposes. As the intervals between observations become shorter, autocorrelation may occur and lead to a high false alarm rate in traditional Statistical Process Control (SPC) charts. In this article, a Multivariate Cuscore (MCuscore) SPC procedure based on the sequential likelihood ratio test and fault signature analysis is developed for monitoring the mean vector of an autocorrelated multivariate process. The MCuscore charts for the transient, steady and ramp mean shift signal are designed; they do not rely on the assumption of known signal starting time. An example is presented to demonstrate the application of the MCuscore chart to monitoring three autocorrelated variables of an online search engine marketing tracking process. Furthermore, the simulation analysis shows that the MCuscore chart outperforms the traditional multivariate cumulative sum control chart in detecting process shifts.