Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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![画像:6.4. The data shown in Table 6E.1 are x and R values for 24 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345). Table 6E.1 Bearing Diameter Data Sample Number Sample x R Number 7 R 1 34.5 3 13 35.4 2 34.2 4 14 34.0 88 6 3 31.6 4 15 37.1 4 31.5 4 16 34.9 5 35.0 5 17 33.5 6 34.1 6 18 31.7 7 32.6 4 19 34.0 8 33.8 3 20 35.1 9 34.8 7 21 33.7 10 33.6 8 22 32.8 11 12 12 31.9 3 23 33.5 38.6 9 24 34.2 5743 842-33 1 a. Set up x and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. Draw x-bar control chart and R chart X1 + x2 + ....... +xm x = ; m ×ばつ = X + A2Ŕ CLx = x LCL = X — A2Ŕ UCLR = DÅR CLR = R LCLR = D3R R R1 + R2 + ··· + Rm ... m Remove the data that are not in control and recalculate UCL, CL, LCL and redraw control chart. b. If specifications on this diameter are 0.5030 ± 0.0010, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed. p=Pr{x <LSL}+Pr{x >USL}=Pr{x <20}+Pr{x >40}=Pr{x <20}+[1–Pr{x <40}]](https://content.bartleby.com/qna-images/question/b3b2a629-b543-4446-b89d-eb00585aef9b/31045099-5c88-40d0-b11f-79b20b9c8af0/tqqf5o_thumbnail.png){kind=link}
Transcribed Image Text:6.4. The data shown in Table 6E.1 are x and R values for 24 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345).
Table 6E.1 Bearing Diameter Data
Sample
Number
Sample
x
R
Number
7
R
1
34.5
3
13
35.4
2
34.2
4
14
34.0
88
6
3
31.6
4
15
37.1
4
31.5
4
16
34.9
5
35.0
5
17
33.5
6
34.1
6
18
31.7
7
32.6
4
19
34.0
8
33.8
3
20
35.1
9
34.8
7
21
33.7
10
33.6
8
22
32.8
11
12
12
31.9
3
23
33.5
38.6
9
24
34.2
5743
842-33
1
a. Set up x and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits.
Draw x-bar control chart and R chart
X1 + x2 + .......
+xm
x =×ばつ = X + A2Ŕ
CLx = x
LCL = X — A2Ŕ
UCLR = DÅR
CLR = R
LCLR = D3R
R
R1 + R2 + ··· + Rm
...
m
Remove the data that are not in control and recalculate UCL, CL, LCL and redraw control chart.
b. If specifications on this diameter are 0.5030 ± 0.0010, find the percentage of nonconforming bearings produced by this process. Assume that diameter is normally distributed.
p=Pr{x <LSL}+Pr{x >USL}=Pr{x <20}+Pr{x >40}=Pr{x <20}+[1–Pr{x <40}]
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