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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?

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  • $\begingroup$ 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 $\endgroup$
    – Glen_b
    Jun 6, 2022 at 23:18
  • $\begingroup$ 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/… $\endgroup$
    – hehe
    Jun 7, 2022 at 16:09

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