The production manager at Sunny Soda, Inc. is interested in tracking the quality of the company’s 12- ounce bottle filling line. The bottles must be filled within the tolerances set for this product because the dietary information on the label shows 12 ounces as the serving size. The design standard for the product calls for a fill level of 12.00 ± 0.10 ounces.

(a) Using the appropriate control charts, explain if the process average and the process range are in control assuming the company uses 3-sigma control limits?

(b) Is this process capable of 5-sigma performance? What statistic helps you reach your conclusion, and what is the value of that statistic?

(c) Explain what action needs to be taken to ensure the process is 5-sigma capable? What statistic helps you reach your conclusion, and what is the value of that statistic? What should be the new value of the parameter you decided to improve?

To facilitate your analysis, use the following table that summarizes the sample data the manager had collected (in fluid ounces per bottle) on the production process:

Observations
Sample 1 2 3 4
1 12.00 11.97 12.10 12.08
2 11.91 11.94 12.10 11.96
3 11.89 12.02 11.97 11.99
4 12.10 12.09 12.05 11.95
5 12.08 11.92 12.12 12.05
6 11.94 11.98 12.06 12.08
7 12.09 12.00 12.00 12.03
8 12.01 12.04 11.99 11.95
9 12.00 11.96 11.97 12.03
10 11.92 11.94 12.09 12.00
11 11.91 11.99 12.05 12.10
12 12.01 12.00 12.06 11.97
13 11.98 11.99 12.06 12.03
14 12.02 12.00 12.05 11.95
15 12.00 12.05 12.01 11.07