The following are X and S values for 20 subgroups of size 5.
|
Subgroup
|
X
|
S
|
Subgroup
|
X
|
S
|
Subgroup
|
X
|
S
|
|
1
|
33.8
|
5.1
|
8
|
36.1
|
4.1
|
15
|
35.6
|
4.8
|
|
2
|
37.2
|
5.4
|
9
|
38.2
|
7.3
|
16
|
36.4
|
4.6
|
|
3
|
40.4
|
6.1
|
10
|
32.4
|
6.6
|
17
|
37.2
|
6.1
|
|
4
|
39.3
|
5.5
|
11
|
29.7
|
5.1
|
18
|
31.3
|
5.7
|
|
5
|
41.1
|
5.2
|
12
|
31.6
|
5.3
|
19
|
33.6
|
5.5
|
|
6
|
40.4
|
4.8
|
13
|
38.4
|
5.8
|
20
|
36.7
|
4.2
|
|
7
|
35.0
|
5.0
|
14
|
40.2
|
6.4
|
|
|
|
(a) Determine trial control limits for an X control chart.
(b) Determine trial control limits for an S-control chart.
(c) Does it appear that the process was in control throughout?
(d) If your answer in part (c) is no, suggest values for upper and lower control limits to be used with succeeding subgroups.
(e) If each item is supposed to have a value within 35 ± 10, what is your estimate of the percentage of items that will fall within this specification?