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

Abstract

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.