The data set shows 48 samples (for 48 hours) of size n=7 collected to test the production process of a filling machine for soft drink bottling.  The target filling is 20 fluid ounces.

Your tasks:

Select a random sample of 24 hours of data.  [Feel free to do it manually, if you cannot use the sample selection procedure in the software. ]       Using the sample data, accomplish the following:

Part 1

1. Construct an x–barchart. Need to use graph paper.
2. Calculate and plot the centerline and upper and lower control limits for the charts.
3. Calculate and plot the A, B and C zone boundaries of the x-bar chart.
4. Plot the 24 sample means on the x-barchart.
5. Based on x-bar findings, is the process under statistical control? Explain and justify your answer.

Part 2

6. Construct an R-chart. Need to use graph paper.
7. Calculate and plot the centerline and upper and lower control limits for the charts.
8. Calculate and plot the A, B and C zone boundaries of the R-chart.
9. Plot the sample ranges on the R-chart.
10. Analyze the pattern of the R-chart.
11. Based on R-chart findings, is the process under statistical control?Explain and justify your answer.

Part 3

12. Theoretically, what is the difference between x-bar chart and R-chart? Explain briefly.
13. How are they used?That is, what is their purpose? Explain briefly.

Part 4

14. Compare the findings from your x-bar chart and R-chart.
15. Explain why rational sub-groupings are used in constructing control charts?
16. What are the major findings from the study? Explain briefly.
17. What are your conclusions from the study?Explain briefly.