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)
