The table below gives information on coded length measurements in a machining process. The data shown are ¯x and R values (coded) for 24 samples of size n = 4. Only the last three decimals of a measurement are recorded (i.e. 24.5 should be 0.30245).
|
Sample no.
|
X
|
R
|
|
1
|
24.5
|
4
|
|
2
|
24.2
|
3
|
|
3
|
21.6
|
3
|
|
4
|
25.5
|
4
|
|
5
|
25.0
|
5
|
|
6
|
24.1
|
6
|
|
7
|
22.6
|
4
|
|
8
|
23.8
|
3
|
|
9
|
24.8
|
7
|
|
10
|
23.6
|
8
|
|
11
|
21.9
|
3
|
|
12
|
28.6
|
9
|
|
Sample no.
|
X
|
R
|
|
13
|
25.4
|
8
|
|
14
|
24.4
|
6
|
|
15
|
24.0
|
5
|
|
16
|
26.8
|
7
|
|
17
|
24.9
|
4
|
|
18
|
23.5
|
3
|
|
19
|
21.7
|
8
|
|
20
|
24.0
|
4
|
|
21
|
25.1
|
2
|
|
22
|
23.7
|
4
|
|
23
|
22.8
|
3
|
|
24
|
23.5
|
2
|
|
sum
|
580
|
115
|
(a) Plot ¯X and R charts based on the data above. What center line and control limits would you recommend for controlling future production? You can assume that out control points are due to assignable causes.
(b) Suppose specifications are 0:30250 _ 0:00100. Calculate cp.
(c) Discuss briefly the capability of the process and how process performance can be improved.