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 UCL× = 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 USL}=Pr{x <20}+Pr{x >40}=Pr{x <20}+[1–Pr{x <40}]
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 UCL× = 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 USL}=Pr{x <20}+Pr{x >40}=Pr{x <20}+[1–Pr{x <40}]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
Related questions
Question
![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
UCL× = 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}]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3b2a629-b543-4446-b89d-eb00585aef9b%2F31045099-5c88-40d0-b11f-79b20b9c8af0%2Ftqqf5o_processed.png&w=3840&q=75)
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 =
;
m
UCL× = 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}]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill