Control Charts for Poisson Count Data with Varying Sample Sizes

• Published in: Journal of quality technology Vol. 42; no. 3; pp. 260 - 275
• Main Authors: Ryan, Anne G., Woodall, William H.
• Format: Journal Article
• Language: English
• Published: Milwaukee, WI Taylor & Francis 01.07.2010; American Society for Quality; Taylor & Francis Ltd
• Subjects: Applied sciences; Average Run Length; Charts; Control charts; Counting; Cumulative Sum Chart; CUSUM charts; Exact sciences and technology; Exponentially Weighted Moving Average Chart; False alarms; Inventory control, production control. Distribution; Mathematical analysis; Methods; Monitoring; Monitors; Operational research and scientific management; Operational research. Management science; Performance evaluation; Poisson distribution; Process controls; Random variables; Sample size; Simulation; Statistical Process Control; Studies; Statistical process control; Control chart; Sample size; Moving average; Average run length; Likelihood ratio; Mean estimation; Poisson process; Steady state; Exponentially Weighted Moving Average Chart; Weighting; Surveillance; CUSUM method; Cumulative Sum Chart; Monitoring
• ISSN: 0022-4065; 2575-6230
• DOI: 10.1080/00224065.2010.11917823

Various cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been recommended to monitor a process with Poisson count data when the sample size varies. We evaluate the ability of these CUSUM and EWMA methods in detecting increases in the Poisson rate by calculating the steady-state average run length (ARL) performance for the charts. Our simulation study indicates that the CUSUM chart based on the generalized likelihood-ratio method is best at monitoring Poisson count data at the out-of-control shift for which it is designed when the sample size varies randomly. We also propose a new EWMA method that has good steady-state ARL performance.