The production manager at Sunny Soda, Inc. is interested in tracking the quality
ID: 376302 • Letter: T
Question
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:
Bottle
Sample 1 2 3 4
1 11.93 12.09 11.99 11.98
2 11.93 11.91 12.01 12.04
3 11.90 12.07 12.08 11.97
4 12.08 12.07 11.97 11.91
5 11.98 11.95 11.92 11.98
6 11.88 12.11 12.09 11.92
7 11.88 11.98 11.86 11.86
8 11.99 11.93 12.10 12.05
9 11.97 11.90 11.92 12.10
10 12.08 12.10 12.14 11.91
11 12.13 12.13 11.96 12.13
12 12.03 12.08 11.95 11.89
13 11.86 12.06 11.98 12.09
14 12.04 12.08 11.98 12.15
15 11.92 12.09 12.10 11.87
Explanation / Answer
Answer A: -
Sample 1 2 3 4 Range X-Bar 1 11.93 12.09 11.99 11.98 0.16 11.97 2 11.93 11.91 12.01 12.04 0.13 11.97 3 11.9 12.07 12.08 11.97 0.18 12.01 4 12.08 12.07 11.97 11.91 0.17 12.01 5 11.98 11.95 11.92 11.98 0.06 11.96 6 11.88 12.11 12.09 11.92 0.23 12 7 11.88 11.98 11.86 11.86 0.12 11.9 8 11.99 11.93 12.1 12.05 0.17 12.1 9 11.97 11.9 11.92 12.1 0.2 11.97 10 12.08 12.1 12.14 11.91 0.23 12.06 11 12.13 12.13 11.96 12.13 0.17 12.09 12 12.03 12.08 11.95 11.89 0.19 11.99 0.401632 13 11.86 12.06 11.98 12.09 0.23 11.99 14 12.04 12.08 11.98 12.15 0.17 12.06 15 11.92 12.09 12.1 11.87 0.23 11.99 0.176 12 Note that the sample size is 4. For the range chart: (D3 = 0, D4 = 2.282) LCL = 0 x 0.176 = 0 UCL = 2.282 x 0.176 = 0.401632 As we can see from the table that all the values of Range are within the values of 0 and 0.4 thus range is in within control Note that the sample size is 4. For the x-bar chart: (A2 = 0.729) UCL = 12 + 0.729 x 0.176 = 12.1283 LCL = 12 - 0.729 x 0.176 = 11.8717 we can see that all of them are within 11.8717 and 12.1283. Therefore, the process is in control.Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.