An adaptive EWMA control chart for monitoring zero-inflated Poisson processes

Abstract

Zero-Inflated Poisson (ZIP) distribution is used to model count data with excessive zeros. In this article, we develop and design an adaptive exponentially weighted moving average (AEWMA) control chart for monitoring ZIP processes. A Markov Chain approach is used to approximate the performance measures; namely the average run length (ARL) and standard deviation of run length (SDRL) of the AEWMA chart. The chart performance is assessed using optimized design parameters that provide the smallest ARL for a range of shifts. A performance comparison of the ZIP-AEWMA chart is conducted with the competing charts in terms of the relative mean index (RMI) metric. Results show that the ZIP-AEWMA chart has superior performance over the competing charts for a wide range of process shifts, especially when the probability of excessive zeros in data is high. The proposed chart is also applied on a real-life application to demonstrate its use. We highly recommend the use of the AEWMA chart for monitoring ZIP processes.

KEYWORDS:

• Adaptive exponentially weighted moving average
• Markov chain
• Optimal design
• Statistical process monitoring
• Zero-inflated Poisson distribution

Acknowledgments

The authors would like to thank the anonymous referees for their insightful comments that improved significantly the manuscript.