Alerts are raised whenever Si exceeds the threshold H; once an alert is raised, we reset the cumulative sum value to be 0. The value of H is determined from the value of K and the average run length (ARL) of the in-control process. The ARL is the average number of time steps before an alert is raised. Whenever the process is operating as expected, the ARL should be large. However, when a shift in the mean occurs, the ARL should be small in order to detect the shift as quickly as possible. The ARL can be determined through a variety of approximating equations, which are summarized in (Montgomery, 2001). According to (Montgomery, 2001), a reasonable value for H is 50, which is five times the standard deviation of the in-control process.
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