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.

KEYWORDS:

• Statistical process control
• distribution-free
• change-point detection
• control chart
• Cucconi test

Acknowledgements

Thanks to the Editor, Associate Editor and two anonymous referees for their valuable comments and constructive suggestions that improve the quality of this work significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper was supported in part by National Natural Science Foundation of China (grants 11501209, 11571113, 11771145, 71602115 and 71772147), Natural Science Foundation of Shanghai (grant 19ZR1414400), the Postdoctoral Science Foundation of China (grants 20160089 and 2015M570348), and the Fundamental Research Funds for the Central Universities (the 111 Project B14019).