A Note on the ARL of Two-Sided Bernoulli-Based CUSUM Control Charts

• Published in: Journal of quality technology Vol. 43; no. 1; pp. 43 - 49
• Main Authors: Megahed, Fadel M., Kensler, Jennifer L. K., Bedair, Khaled, Woodall, William H.
• Format: Journal Article
• Language: English
• Published: Milwaukee, WI Taylor & Francis 01.01.2011; American Society for Quality; Taylor & Francis Ltd
• Subjects: Applied sciences; Average Run Length; Bernoulli CUSUM; Bernoulli Hypothesis; Control charts; CUSUM charts; Documents; Equality; Exact sciences and technology; Heart surgery; Industrial applications; Inventory control, production control. Distribution; Monitoring; Mortality; Operational research and scientific management; Operational research. Management science; Patients; Probability; Process controls; Risk-Adjustment; Statistical Process Control; Statistics; Studies; Surgical Outcomes; Statistical process control; Control chart; Risk-Adjustment; Surveillance; Bernoulli CUSUM; Surgical Outcomes; Surgery; Average run length; Risk management; Monitoring; Public health
• ISSN: 0022-4065; 2575-6230
• DOI: 10.1080/00224065.2011.11917844

In this article, we examine the average run length (ARL) properties of two types of two-sided Bernoulli cumulative sum (CUSUM) control charts. In particular, we give the conditions under which the ARL of the two-sided Bernoulli CUSUM chart can be determined exactly from the ARLs of the corresponding upper and lower Bernoulli CUSUM charts. This ARL relationship is established for both the standard industrial application and the risk-adjusted health-care monitoring application.