The Precision Machining Company makes hand-held tools on an assembly line that produces one product every minute. On one of the products, the critical quality dimension is the diameter (measured in thousandths of an inch) of a hole bored in one of the assemblies. Management wants to detect any shift in the process average diameter from 0.010 in. Management considers the variance in the process to be in control. Historically, the average range has been 0.002 in., regardless of the process average. Design an x-chart to control this process, with a center line at 0.010 in. and the control limits set at three sigmas from the center line. Management provided the results of 80 minutes of output from the production line, as shown in the table below. During these 80 minutes, the process average changed once. All measurements are in thousandths of an inch. Sample data for Precision Machining Company Diameter (thousandths of an inch) 10 9 Minutes 9 11 1- 12 13-24 25 - 36 37 - 48 10 10 11 13 12 9. 8 11 12 11 12 11 9 8 9 10 11 10 12 9 8 10 12 13 10 11 10 10 11 12 13 11 10 11 11 12 13 14 10 11 10 49 - 60 7 12 11 10 8 12 10 9 11 10 12 13 12 9 61- 72 10 11 12 13 9. 11 10 13 73- 80 11 13 12 13 11 12 12 a. Set up an x-chart with n= 4. The frequency should be sample four and then skip four. Thus, your first sample would be for minutes 1-4, the second would be for minutes 9- 12, and so on. Compute the mean, x, for each sample. (Enter your responses rounded to two decimal places.) - X Reference Sample Minutes 1-4 10.75 2 9- 12 Factors for calculating three-sigma limits for the x-chart. 17- 20 25 - 28 10.00 8.75 9.75 3 Size of Sample Factor for UCL and LCL (n) 4 for x-chart (A,) 33- 36 10.50 6. 41-44 11.25 2 1.880 3 1.023 7 49 - 52 57 - 60 9.75 0.729 8 11.00 5 0.577 9 65 - 68 0.483 0.419 6. 10 73-76 12.25 0.373 0.337 The UCL; equals minutes and the LCL, equals minutes. (Enter your responses rounded to two decimal places.) 10 0.308 Print Done
The Precision Machining Company makes hand-held tools on an assembly line that produces one product every minute. On one of the products, the critical quality dimension is the diameter (measured in thousandths of an inch) of a hole bored in one of the assemblies. Management wants to detect any shift in the process average diameter from 0.010 in. Management considers the variance in the process to be in control. Historically, the average range has been 0.002 in., regardless of the process average. Design an x-chart to control this process, with a center line at 0.010 in. and the control limits set at three sigmas from the center line. Management provided the results of 80 minutes of output from the production line, as shown in the table below. During these 80 minutes, the process average changed once. All measurements are in thousandths of an inch. Sample data for Precision Machining Company Diameter (thousandths of an inch) 10 9 Minutes 9 11 1- 12 13-24 25 - 36 37 - 48 10 10 11 13 12 9. 8 11 12 11 12 11 9 8 9 10 11 10 12 9 8 10 12 13 10 11 10 10 11 12 13 11 10 11 11 12 13 14 10 11 10 49 - 60 7 12 11 10 8 12 10 9 11 10 12 13 12 9 61- 72 10 11 12 13 9. 11 10 13 73- 80 11 13 12 13 11 12 12 a. Set up an x-chart with n= 4. The frequency should be sample four and then skip four. Thus, your first sample would be for minutes 1-4, the second would be for minutes 9- 12, and so on. Compute the mean, x, for each sample. (Enter your responses rounded to two decimal places.) - X Reference Sample Minutes 1-4 10.75 2 9- 12 Factors for calculating three-sigma limits for the x-chart. 17- 20 25 - 28 10.00 8.75 9.75 3 Size of Sample Factor for UCL and LCL (n) 4 for x-chart (A,) 33- 36 10.50 6. 41-44 11.25 2 1.880 3 1.023 7 49 - 52 57 - 60 9.75 0.729 8 11.00 5 0.577 9 65 - 68 0.483 0.419 6. 10 73-76 12.25 0.373 0.337 The UCL; equals minutes and the LCL, equals minutes. (Enter your responses rounded to two decimal places.) 10 0.308 Print Done
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text:The Precision Machining Company makes hand-held tools on an assembly line that produces one product every minute. On one of the products, the critical quality dimension is the
diameter (measured in thousandths of an inch) of a hole bored in one of the assemblies. Management wants to detect any shift in the process average diameter from 0.010 in.
Management considers the variance in the process to be in control. Historically, the average range has been 0.002 in., regardless of the process average. Design an x-chart to control
this process, with a center line at 0.010 in. and the control limits set at three sigmas from the center line.
Management provided the results of 80 minutes of output from the production line, as shown in the table below. During these 80 minutes, the process average changed once. All
measurements are in thousandths of an inch.
Sample data for Precision Machining Company
Diameter (thousandths of an inch)
9
Minutes
1- 12
10
10
9
13
12
10
8.
9
8
12
12
12
10
9.
13
11
11
11
13-24
25 - 36
37 - 48
12
9
10
9
11
11
11
10
8
12
13
10
10
10
10
10
11
11
13
11
10
11
11
12
13
14
11
49 - 60
61 - 72
73- 80
7
10
12
13
12
12
11
9
9
11
10
12
10
11
12
13
8
10
9.
9
11
10
11
13
12
13
11
12
9
12
a. Set up an x-chart with n = 4. The frequency should be sample four and then skip four. Thus, your first sample would be for minutes 1-4, the second would be for minutes 9- 12, and
so on.
Compute the mean, x, for each sample. (Enter your responses rounded to two decimal places.)
- X
Reference
Sample
Minutes
1
1-4
10.75
2
3
Factors for calculating three-sigma limits for the x-chart.
9- 12
10.00
17 - 20
8.75
25 - 28
33 - 36
Size of Sample Factor for UCL and LCL
(n)
4
9.75
for x-chart (A2)
10.50
2
1.880
41- 44
49 - 52
57 - 60
6
11.25
7.
3
1.023
9.75
11.00
4
0.729
0.577
9
65 - 68
9
6
0.483
10
73- 76
12.25
7
0.419
8
0.373
0.337
The UCL; equals minutes and the LCL, equalsminutes. (Enter your responses rounded to two decimal places.)
10
0.308
Print
Done
Transcribed Image Text:b. Set up an x-chart with n= 8. The frequency should be sample eight and then skip four.
Compute the mean, x, for each sample. (Enter your responses rounded to two decimal places.)
Sample
Minutes
1
1-8
10.63
13 - 20
9.88
3
25 - 32
10.38
4
37 - 44
11.25
49 - 56
10.13
6
61- 68
10.25
7
73 - 80
11.63
The UCL; equals
minutes and the LCL, equals
minutes. (Enter your responses rounded to two decimal places.)
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