Average run length
= Average run length
{title2=$\operatorname{ARL}=\mathbb E\inf\{t\geq1:C_t\geq h\}$}
The average run length of a <CUSUM> is the <expectation> of its first signalling time under a specified data model and initial chart state. A large in-control average run length discourages false alarms; a small out-of-control value indicates rapid detection. The mean alone does not give a finite-horizon <Type I error> probability or the complete detection-delay distribution.