This article examines the average run length (ARL) properties of two different kinds of two-sided Bernoulli cumulative sum (CUSUM) control charts. It describes the conditions under which the ARL can be determined precisely from the ARLs of the upper and lower Bernoulli CUSUM charts. This relationship is established for both the standard industrial application of the two-sided Bernoulli CUSUM and the risk-adjusted application for health care monitoring.
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