Question 10.10: Rolls of sheet aluminum, used to manufacture cans, are exami...
Rolls of sheet aluminum, used to manufacture cans, are examined for surface flaws. Table 10.3 presents the numbers of flaws in 40 samples of 100 m² each. Compute the center line and 3σ control limits for the c chart. Plot the chart. Does the process appear to be in control?
TABLE 10.3 Number of flaws, for Example 10.10 | |||||||
Sample | Number of Flaws (c) | Sample | Number of Flaws (c) | Sample | Number of Flaws (c) | Sample | Number of Flaws (c) |
1 | 16 | 11 | 14 | 21 | 11 | 31 | 10 |
2 | 12 | 12 | 11 | 22 | 16 | 32 | 10 |
3 | 9 | 13 | 10 | 23 | 16 | 33 | 10 |
4 | 13 | 14 | 9 | 24 | 13 | 34 | 12 |
5 | 15 | 15 | 9 | 25 | 12 | 35 | 14 |
6 | 5 | 16 | 14 | 26 | 17 | 36 | 10 |
7 | 13 | 17 | 10 | 27 | 15 | 37 | 15 |
8 | 11 | 18 | 12 | 28 | 13 | 38 | 12 |
9 | 15 | 19 | 8 | 29 | 15 | 39 | 11 |
10 | 12 | 20 | 14 | 30 | 13 | 40 | 14 |
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The average of the 40 counts is \bar{c } = 12.275. The center line is therefore plotted at 12.275. The 3σ control limits are plotted at 12.275 ± 3 \sqrt{12.275}. The upper control limit is therefore 22.7857, and the lower control limit is 1. 7643. Figure 10.15 presents the c chart. The process appears to be in control.

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