Twelve samples, 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:

(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 whynot?

Sample Mean (in.) 10.002 10.002 9.991 10.006 9.997 9.999 10.001 0.005 9.995 10.001 10.001 10.006 Range (in.) 0.011 0.014 0.007 0.022 0.013 0.012 0.008 0.013 0.004 0.011 0.014 0.009 Sample 10 12