A Directional Multivariate Sign EWMA Control Chart

In many applications the shift directions of observation vectors are limited, which allows focusing detection power on a limited subspace with improved sensitivity. This paper develops a new multivariate nonparametric statistical process control chart for monitoring location parameters, which is based on integrating a directional multivariate spatial-sign test and exponentially weighted moving average control scheme to on-line sequential monitoring. The computation speed of the proposed scheme is fast with a similar computation effort to its parametric counterpart, regression-adjusted control charts. It has a distribution-free property over a broad class of population models, which implies the in-control run length distribution can attain or is always very close to the nominal one when using the same control limit designed for a multivariate normal distribution. This proposed control chart possesses some other appealing features. Simulation studies show that it is efficient in detecting small or moderate shifts, when the process distribution is heavy-tailed or skewed. Finally, a specific SPC example, multistage process control, is also presented to demonstrate the effectiveness of our method.