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

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

Part 2

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

Part 3

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

Part 4

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

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