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
 

Attachments

  • XBar Chart.jpeg
    XBar Chart.jpeg
    21.3 KB · Views: 453
  • QualityIndex1180.xls
    16.5 KB · Views: 189
Physics news on Phys.org
  • #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.
 

1. What is a Quality Control Chart?

A Quality Control Chart is a graphical representation of data that is used to monitor and analyze the performance of a process over time. It helps identify any patterns or trends in the data that may indicate a deviation from expected quality levels.

2. What are the Upper and Lower Limits in a Quality Control Chart?

The Upper and Lower Limits in a Quality Control Chart represent the boundaries within which the process is expected to perform. These limits are based on the average performance of the process and are used to determine if the process is running within acceptable quality levels.

3. How do you calculate the Upper and Lower Limits in a Quality Control Chart with R?

The Upper and Lower Limits in a Quality Control Chart can be calculated using the R statistical software. The Upper Limit is calculated by adding three times the standard deviation to the process mean, and the Lower Limit is calculated by subtracting three times the standard deviation from the process mean.

4. Why is it important to monitor the Upper and Lower Limits in a Quality Control Chart?

Monitoring the Upper and Lower Limits in a Quality Control Chart is important because it allows for the early detection of any deviations from expected quality levels. This can help prevent defects, reduce waste, and improve overall process performance.

5. What should be done if the data falls outside of the Upper and Lower Limits in a Quality Control Chart?

If the data falls outside of the Upper and Lower Limits in a Quality Control Chart, it may indicate that the process is not performing within acceptable quality levels. In this case, further investigation and corrective actions should be taken to identify and address the root cause of the issue.

Hot Threads

Recent Insights

Back
Top