A circular shaft is machined on a numerically controlled lathe; the target diameter for the shaft is 37.50 mm, the upper specification limit is 37.55 mm and the lower specification limit is 37.45 mm. Measurements x of shaft diameter are shown in Table 1; these are arranged in 25 sub-groups each containing 5 individuals. For n = 5, A2 = 0.58, D3 = 0.0, Da= 2.11, d2 = 2.326 a) Estimate lower and upper control limits for means and ranges. b) Plot control charts for means and ranges. c) Estimate process capability index Cp.
A circular shaft is machined on a numerically controlled lathe; the target diameter for the shaft is 37.50 mm, the upper specification limit is 37.55 mm and the lower specification limit is 37.45 mm. Measurements x of shaft diameter are shown in Table 1; these are arranged in 25 sub-groups each containing 5 individuals. For n = 5, A2 = 0.58, D3 = 0.0, Da= 2.11, d2 = 2.326 a) Estimate lower and upper control limits for means and ranges. b) Plot control charts for means and ranges. c) Estimate process capability index Cp.
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Transcribed Image Text:A circular shaft is machined on a numerically controlled lathe; the target diameter
for the shaft is 37.50 mm, the upper specification limit is 37.55 mm and the lower
specification limit is 37.45 mm.
Measurements x of shaft diameter are shown in Table 1; these are arranged in 25
sub-groups each containing 5 individuals. For n = 5, A2 = 0.58,
D3 = 0.0, D4= 2.11, d2 = 2.326
a) Estimate lower and upper control limits for means and ranges.
b) Plot control charts for means and ranges.
c) Estimate process capability index Cp.
Transcribed Image Text:Table 1: Measurements of shaft diameter - All units are in mm.
Sub-group
no. j
2
3
4
6
7
10
11
12
13
Individual
no. i
0.49
0.51
0.51
0.48
0.50
0.48
0.51
0.48
0.49
0.48
0.52
0.53
0.50
2
0.50
0.53
0.52
0.50
0.51
0.51
0.52
0.50
0.52
0.50
0.51
0.51
0.50
3
0.49
0.51
0.52
0.50
0.49
0.51
0.49
0.52
0.53
0.48
0.54
0.53
0.51
4
0.49
0.53
0.50
0.51
0.53
0.53
0.51
0.51
0.53
0.52
0.46
0.49
0.51
5
0.53
0.49
0.51
0.49
0.52
0.50
0.50
0.51
0.57
0.49
0.52
0.50
0.50
Means X,
0.50
0.51
0.51
0.50
0.51
0.51
0.51
0.50
0.52
0.49
0.51
0.51
0.50
Ranges R,
0.04
0.04
0.02
0.03
0.04
0.05
0.03
0.04
0.04
0.04
0.08
0.04
0.01
Sub-group no./
14
15
16
17
18
19
20
21
22
23
24
25
Individual
по.
1
0.49
0.54
0.51
0.51
0.51
0.49
0.48
0.46
0.48
0.52
0.49
0.49
0.50
0.52
0.52
0.5
0.5
0.49
0.48
0.47
0.52
0.49
0.48
0.50
3
0.53
0.52
0.51
0.53
0.48
0.53
0.49
0.49
0.49
0.51
0.49
0.50
4
0.51
0.51
0.52
0.5
0.5
0.49
0.48
0.52
0.49
0.49
0.48
0.48
0.48
0.53
0.49
0.52
0.48
0.50
0.49
0.52
0.51
0.49
0.50
0.49
Means X,
Ranges R,
0.50
0.52
0.51
0.51
0.49
0.50
0.48
0.49
0.50
0.50
0.49
0.49
0.05
0.03
0.03
0.03
0.03
0.04
0.01
0.06
0.04
0.03
0.02
0.02
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