A window-limited generalized likelihood ratio test for monitoring Poisson processes with linear drifts

Abstract

There is gradually increasing attention devoted to the monitoring of Poisson process due to its wide applications in industry quality control and health-care surveillance. However, most of the study focuses on the case with step shifts in Poisson means. Relatively little attention has been paid to the case with linear drifts in Poisson means. This paper extends the window-limited generalized likelihood ratio (WGLR) test from the monitoring of normal means to Poisson processes, with focus on linear drifts. The comparison results with the adaptive cumulative sum (ACUSUM) charts and the weighted CUSUM (WCUSUM) charts show that the WGLR chart generally provides better detection performance than the other alternative methods in both the zero-state and steady-state cases.

Keywords:

• adaptive CUSUM
• average run length
• generalized likelihood ratio
• linear drifts
• weighted CUSUM

Acknowledgements

We are grateful to the anonymous referees for their insightful suggestions that help significantly improve the quality of this paper. Lianjie Shu's work was support in part by FDCT/002/2013/A and MYRG090(Y1-L2)-FBA13-SLJ. Kowk-Leung Tsui's research was supported by the Research Fund for the Control of Infectious Diseases, granted by the Food and Health Bureau, HKSAR (Ref. 11101262); the Collaborative Research Fund, granted by the Research Grants Council (Ref. CityU8/CRF/12G).