Average run length ($\mathrm{ARL}=\mathbb{E}\inf \{t\ge 1:C_t\ge h\}$)

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.