Solving Quality Control Chart Upper & Lower Limit with R

In summary: Hope that helps!In summary, the conversation revolved around calculating the Upper and Lower Control Limits on an R chart using different formulas in R and the qcc package. It was mentioned that the formula used for an individual range chart may differ from the formula used for a standard Xbar-R chart, which could explain the discrepancies in the calculated Upper Limit. It was suggested to check the sample size and refer to a table to determine the appropriate value for A2.
  • #1
Apple&Orange
30
2
Hi all
I'm having a bit of trouble trying to calculate the Upper and Lower Control Limit on R chart.

The file "QualityIndex1180" contains the information from which I'm doing my calculations. Ob1, Ob2, and Ob3 are basically 3 samples that have been taken the first of 15 batches on some production process.

Using R, I calculated the grand mean, xbarbar, to be 733/45. Using that, I calculated the Upper Limit to be 16.87 from the formula UCL=Xbarbar-A2*Rbar, where Rbar is 197/75 and A2 is 0.223.
However, using the qcc package on R, and on Minitab, it shows the Upper limit is 18.976

I'm confused to as why its 18.976 instead of 16.87

Cheers
Apple&Orange
 

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  • #2
You may be using different formulas in R and the qcc package. The formula you gave is used to calculate the control limit for an individual range chart, while the qcc package is probably using the formula for a standard Xbar-R chart. The formula for the Upper Control Limit for a standard Xbar-R chart is given by UCL = Xbarbar + A2*Rbar, where A2 is a value from a table depending on the sample size. You can look up the value of A2 for your sample size in this table: https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc32.htm.
 

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