Nonparametric multivariate control charts based on a linkage ranking algorithm

Control charts have been widely recognized as important and critical tools in system monitoring for detection of abnormal behavior and quality improvement. In particular, multivariate control charts have been effectively used when a process involves a number of correlated quality characteristics. Most existing multivariate control charts were developed using the assumption of normally distributed quality characteristics. However, process data from modern industries often do not follow the normal distribution. Despite the great need for nonparametric control charts that can control the error rate regardless of the underlying distribution, few efforts have been made in this direction. In this paper, we propose a new nonparametric control chart (called the kLINK chart) based on a k-linkage ranking algorithm that calculates the ranking of a new observation relative to the in-control training data. A simulation study was performed to demonstrate the effectiveness of our kLINK chart and its superiority over the traditional Hotelling's T² chart and the ranking depth control chart in nonnormal situations. In addition, to enable increased sensitivity to small shifts, we present an exponentially weighted moving average version of a kLINK chart.