Among the various procedures used to detect potential changes in a stochastic
process the moving sum algorithms are very popular due to their intuitive
appeal and good statistical performance. One of the important design parameters
of a change detection algorithm is the expected interval between false
positives, also known as the average run length (ARL). Computation of the ARL
usually involves numerical procedures but in some cases it can be approximated
using a series involving multivariate probabilities.