Twelve sample, each containing five 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 results 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) Determine the upper and lower control limits and the overall means for x-charts and R-charts.
b) Draw the charts and plot the values of the sample means and ranges.
c) Do the data indicate a process that is in control?
d) Why or why not?