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Why do we compute the control limits for the individuals or XmR chart with an estimated sigma, 2.66 x mR(avg)? I understand that the overall population sigma is different. But why is one more appropriate than the other?

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If you simply use three sigma limits you're not considering the possibility your data is not homogeneous. This article I eventually found explains it well.

https://www.qualitydigest.com/inside/twitter-ed/individual-charts-done-right-and-wrong.html

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