Twenty subgroups of size 5 are obtained for the purpose of determining
trial control limits for an X- and an R-chart. The data are as follows.
Subgroup Subgroup
Number X R Number X R
1 23 5 11 26 5
2 22 3 12 21 4
3 24 2 13 22 4
4 20 4 14 20 4
5 18 3 15 23 3
6 17 4 16 21 6
7 24 4 17 20 5
8 10 3 18 18 4
9 16 5 19 15 3
10 20 4 20 17 2
(a) Determine the trial control limits for each chart.
(b) Explain why there are so many subgroup averages outside the control
limits for the X-chart in spite of the fact that the averages do not vary
greatly.
(c) What should be done with those subgroups whose average is beyond
the limits?
(d) Since the number of points outside the control limits on the X-chart is
quite high relative to the number of points that are plotted, what might
this suggest a
