A new nonparametric monitoring of data streams for changes in location and scale via Cucconi statistic

Abstract

Many distribution-free control charts have been proposed for jointly monitoring location and scale parameters of a continuous distribution when their in-control (IC) status are unknown in advance. Unfortunately, most existing methods require relatively large amount of historical observations to estimate the IC parameters or to activate the control chart, and batch observations to construct the charting statistic. When such assumptions are invalid, they may not be reliable for online monitoring. In this paper, we propose a novel distribution-free control chart for joint monitoring of location and scale parameters with extremely small IC sample size. The proposed control chart integrates the Cucconi test into the framework of change-point detection and exponentially weighted moving average strategy. It requires no prior knowledge of the underlying distribution, and is very robust in start-up situations. Comprehensive numerical results show that the proposed chart is superior to its competitors.