A nonparametric CUSUM chart for monitoring multivariate serially correlated processes

In applications, most processes for quality control and management are multivariate. Thus, multivariate statistical process control (MSPC) is an important research problem and has been discussed extensively in the literature. Early MSPC research is based on the assumptions that process observations at different time points are independent and they have a parametric distribution (e.g., Gaussian) when the process is in-control (IC). Recent MSPC research has lifted the "parametric distribution" assumption, and some nonparametric MSPC charts have been developed. These nonparametric MSPC charts, however, often requires the "independent process observations" assumption, which is rarely valid in practice because serial data correlation is common in a time series data. In the literature, it has been well demonstrated that a control chart who ignores serial data correlation would be unreliable to use when such data correlation exists. So far, we have not found any existing nonparametric MSPC charts that can accommodate serial data correlation properly. In this paper, we suggest a flexible nonparametric MSPC chart which can accommodate stationary serial data correlation properly. Numerical studies show that it performs well in different cases.