Nancy, Inc. manufactures 4 ounce chocolate bars. Random samples of size four wer

Question

Nancy, Inc. manufactures 4 ounce chocolate bars. Random samples of size four were taken and weighed. Eight hours of observation provided the following data.
Sample       Mean       Range

1                4.01          0.14

2                4.03          0.18

3                3.98          0.16

4                 4.20          0.17

5                 3.89          0.13

6                4.00         0.18

7                4.05          0.17

8                 4.03          0.16

9                4.08          0.15

a. Determine the 3 sigma upper and lower control limits for the x-bar chart.

b. Determine the 3 sigma upper and lower control limits for the R-chart.

Explanation / Answer

Avg Range

R-bar

Each sample size n=4

Total no of samples = 9

UCL (X-bar) = X-bar-bar + (A2 x R-bar)= 4.03+ 0.729 * 0.16= 4.146

LCL(X-bar) = X-bar-bar - (A2 x R-bar) = 4.03- 0.729 * 0.16 = 3.91

UCL (R) = R-bar x D4 = 0.16 * 2.282= 0.36512

There is no Lower Control Limit for the Range Chart if the subgroup size is 6 or less

Mean Range 1 4.01 0.14 2 4.03 0.18 3 3.98 0.16 4 4.2 0.17 5 3.89 0.13 6 4 0.18 7 4.05 0.17 8 4.03 0.16 9 4.08 0.15 Avg Mean X-bar-bar

Avg Range

R-bar

4.03 0.16

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