# What is the rationale of using 2.66 times moving range for control limits in individual control charts?

The Wikipedia says "If the data are normally distributed with standard deviation $$\sigma$$ then the expected value of $$\overline {MR}$$ is $$d_{{2}}\sigma =2\sigma /{\sqrt \pi }$$."

https://en.wikipedia.org/wiki/Shewhart_individuals_control_chart

Are the control limits based on moving range robust to violation of the normal distribution assumption?

• I replaced  by \$and removed the duplication of formulas inherent in the way Wikipedia does it. Note that in the same article it says "The value$2.66$is obtained by dividing$3$by the sample size-specific$d_2$anti-biasing constant for$n=2$, as given in most textbooks on statistical process control (see, for example, Montgomery)", which adds a little information about where it comes from Jun 6, 2022 at 23:18 • thanks! Realize I should use$ instead of  for formulae now. This post helps explain the convergence of 2.66MR to 3sigma. stats.stackexchange.com/questions/288486/…
– hehe
Jun 7, 2022 at 16:09