12 samples, each containing 5 parts, were taken from a process that produces steel rods.

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12 samples, each containing 5 parts, were taken from a process that produces steel rods. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The result were:
Sample
Sample Mean (in)
Range (in)
1
10.002
0.011
2
10.002
0.014
3
9.991
0.007
4
10.006
0.022
5
9.997
0.013
6
9.999
0.012
7
10.001
0.008
8
10.005
0.013
9
9.995
0.004
10
10.001
0.011
11
10.001
0.014
12
10.006
0.009
a) Using the data in the table, compute the center line, the upper control limit, and lower control limit for the and R charts. (10 Marks)
(Note: Refer to Appendix 1 for the formula)
b) Is the process in control? Interpret the charts. (6 Marks)
c) If the specification is 10.000± 0.005 compute the index process capability Cp and Cpk. Interpret the result. (4 Marks)

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