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Risk-adjusted charts for monitoring a surgical or patient care process have recently gained prominence in the literature. To monitor a patient care process, especially to detect deterioration is crucial in saving patients' lives. In this paper, a new charting procedure is developed for monitoring a patient care process for patients admitted to a hospital with acute myocardial infarctions. This procedure is based on the number-between failures by taking the patients' risks into account. When there is a change in the risk distribution of incoming patients, it is demonstrated that this procedure will behave properly while the non-risk-adjusted counterpart will signal incorrectly that the patient care process has changed. The setting up of this chart to monitor a patient care process for patients with acute myocardial infarctions is described in detail.