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I am learning a Quality Control course and in theory part I don't understand calculating the control limits for $\bar{x}$ and R chart.I want to know, say when I calculate the R chart control limits no points plot outside the control limit.And therefore using this $\bar{R} $ values I can then go to calculate $\bar{x} $ chart control limits.In that say 2 sample values are plotted outside the control limits and in each of these suppose an assignable cause was found.Therefore we have to remove this point and recalculate control limits for $\bar{x}$ chart.My question is do I have to recalculate the R chart control limits also.Because now in $\bar{x}$ chart 2 samples are removed.Or do I use the earlier $\bar{R} $value and use removing the two samples only recalculate $\bar{x}$?

Also say there's a pattern is present like a cycle or a shift in process level.Even if all the points lie inside the control limit with the presence of a pattern does it indicate that the process is out of control?Or is the process in control, but some factor affects to shift the process level?

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Yes you have to recalculate the R chart control limits as well. Even though there is no point outside the control limits in R chart, removal of two points due to x-bar chart changes the control limits of R chart. For the second part, if there is a pattern or a cycle you can say that the system is not in statistical control. Therefore you have to look for an assignable cause

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  • $\begingroup$ If the class did not cover it, there are sets of rules for determining if a chart is in statistical control. The most popular set are the Western Electric Rules. Also, I would suggest that if you are willing to accept @Bob's answer that you accept the answer in the system. $\endgroup$
    – Tavrock
    Dec 7, 2016 at 23:25

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