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:
|
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?