A Combination of CUSUM Charts for Monitoring a Zero-Inflated Poisson Process

Abstract

The Zero-inflated Poisson distribution (ZIP) is used to model the defects in processes with a large number of zeros. We propose a control charting procedure using a combination of two cumulative sum (CUSUM) charts to detect increases in the parameters of ZIP process, one is a conforming run length (CRL) CUSUM chart and another is a zero truncated Poisson (ZTP) CUSUM chart. The control limits of the control charts are obtained using both Markov chain-based methods and simulations. Simulation experiments show that the proposed method outperforms an existing method. Finally, a real example is presented.

Keywords:

• Average number of observations to signal
• CUSUM chart
• Markov chain
• ZIP process

Mathematics Subject Classification:

• Primary 65C60
• Secondary 68U20

Acknowledgments

The authors thank the editor and referees for their helpful comments that improved this paper significantly. This research was supported by National Natural Science Foundation of China (NSFC) with grant nos. 71002105, 70931004, and 71225006.