The fill volume of soft-drink beverage bottles is an important quality characteristic. The volume is measured (approximately) by placing a gauge over the crown and comparing the height of the liquid in the neck of the bottle against a coded scale. On this scale, a reading of zero corresponds to the correct fill height. Fifteen samples of size n= 6 have been analyzed, and the fill heights are shown in the following table. Sample Number X2 X3 X4 X5 X6 1 0.5 -1.0 2.5 -1.0 2.0 0.5 2 0.5 1.5 1.0 -1.0 1.5 3 1.5 1.0 0.0 -1.0 -1.0 1.0 4 -2.0 0.0 -1.0 1.5 0.0 -2.0 5 0.0 -0.5 0.5 1.0 -0.5 0.0 6 0.0 0.0 0.0 0.5 1.0 -2.0 1.0 -1.0 0.0 1.5 1.0 0.0 8. -0.5 1.5 0.0 0.0 -1.0 0.5 9 1.5 1.5 0.0 0.0 1.0 0.0 10 0.0 -1.0 -1.5 -1.5 -1.0 1.0 11 0.0 0.0 2.0 -1.5 -0.5 2.0 12 -0.5 0.0 -0.5 2.0 0.0 0.5 13 -0.5 -1.0 0.0 0.5 -1.5 -1.0 14 -1.0 -0.5 -2.0 -1.0 0.0 1.5 15 1.5 1.5 1.0 -1.0 1.0 -2.0 (a) Set up ī and s control charts on this process. Does the process exhibit statistical control? If necessary, construct revised control limits. (b) Construct x and R chart, and compare with the s chart in part (a).

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3. The fill volume of soft-drink beverage bottles is an important quality characteristic. The volume is
measured (approximately) by placing a gauge over the crown and comparing the height of the liquid
in the neck of the bottle against a coded scale. On this scale, a reading of zero corresponds to the
correct fill height. Fifteen samples of size n= 6 have been analyzed, and the fill heights are shown
in the following table.
Sample
Number
x2
X3
X4
X5
X6
1
0.5 -1.0
2.5
-1.0
2.0
0.5
2
0.5
1.5
1.0
-1.0
1.5
3
1.5
1.0
0.0
-1.0 -1.0
1.0
4
-2.0
0.0 -1.0
1.5
0.0
-2.0
0.0 -0.5
0.5
1.0
-0.5
0.0
0.0
0.0
0.0
0.5
1.0
-2.0
7
1.0 -1.0
0.0
1.5
1.0
0.0
8
-0.5
1.5
0.0
0.0 -1.0
0.5
9
1.5
1.5
0.0
0.0
1.0
0.0
10
0.0 -1.0 -1.5
-1.5
-1.0
1.0
11
0.0
0.0
2.0
-1.5
-0.5
2.0
12
-0.5
0.0 -0.5
2.0
0.0
0.5
13
-0.5 -1.0
0.0
0.5 -1.5
-1.0
14
-1.0 -0.5 -2.0
-1.0
0.0
1.5
15
1.5
1.5 1.0 -1.0
1.0 -2.0
(a) Set up ī and s control charts on this process. Does the process exhibit statistical control? If
necessary, construct revised control limits.
(b) Construct x and R chart, and compare with the s chart in part (a).
Transcribed Image Text:3. The fill volume of soft-drink beverage bottles is an important quality characteristic. The volume is measured (approximately) by placing a gauge over the crown and comparing the height of the liquid in the neck of the bottle against a coded scale. On this scale, a reading of zero corresponds to the correct fill height. Fifteen samples of size n= 6 have been analyzed, and the fill heights are shown in the following table. Sample Number x2 X3 X4 X5 X6 1 0.5 -1.0 2.5 -1.0 2.0 0.5 2 0.5 1.5 1.0 -1.0 1.5 3 1.5 1.0 0.0 -1.0 -1.0 1.0 4 -2.0 0.0 -1.0 1.5 0.0 -2.0 0.0 -0.5 0.5 1.0 -0.5 0.0 0.0 0.0 0.0 0.5 1.0 -2.0 7 1.0 -1.0 0.0 1.5 1.0 0.0 8 -0.5 1.5 0.0 0.0 -1.0 0.5 9 1.5 1.5 0.0 0.0 1.0 0.0 10 0.0 -1.0 -1.5 -1.5 -1.0 1.0 11 0.0 0.0 2.0 -1.5 -0.5 2.0 12 -0.5 0.0 -0.5 2.0 0.0 0.5 13 -0.5 -1.0 0.0 0.5 -1.5 -1.0 14 -1.0 -0.5 -2.0 -1.0 0.0 1.5 15 1.5 1.5 1.0 -1.0 1.0 -2.0 (a) Set up ī and s control charts on this process. Does the process exhibit statistical control? If necessary, construct revised control limits. (b) Construct x and R chart, and compare with the s chart in part (a).
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