For process monitoring, the EWMA (Exponentially Weighted Moving Average) and DEWMA (Double EWMA) control charts are widely used to detect small shifts in the process mean. The ARL (Average Run Length) measures the average number of samples taken before an out-of-control signal.

Here are some resources and example R packages/functions you can use:

• The qcc package in R provides functions for EWMA control charts:

library(qcc)

data

EWMA calculation formula is

EMA (t)=α * X (t)+(1- α) * EMA (t-1)

where α is the attenuation factor