1.8 A Canadian manufacturer identified a critical diameter on a crank bore that needed to be maintained within a close tolerance for the product to be successful. Sam- ples of size 4 were taken every hour. The values of the differences (measurement — specification), in ten- thousandths of an inch, are given in Table 1.4. (a) Calculate the central line for an X-bar chart for the 24 hourly sample means. The centerline is x = — . . . (4.25 -3.00 -1.50 +3.25)/24. = (b) Is the average of all the numbers in the table, 4 for each hour, the same as the average of the 24 hourly averages? Should it be? (c) A computer calculation gives the control limits LCL = -4.48 UCL 7.88 = Construct the X-bar chart. Identify hours where the process was out of control.

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1.8 A Canadian manufacturer identified a critical diameter
on a crank bore that needed to be maintained within a
close tolerance for the product to be successful. Sam-
ples of size 4 were taken every hour. The values of
the differences (measurement - specification), in ten-
thousandths of an inch, are given in Table 1.4.
(a) Calculate the central line for an X-bar chart for
the 24 hourly sample means. The centerline is
x = — . . .
(4.25 -3.00 -1.50 +3.25)/24.
=
(b) Is the average of all the numbers in the table, 4 for
each hour, the same as the average of the 24 hourly
averages? Should it be?
(c) A computer calculation gives the control limits
LCL = -4.48
UCL 7.88
=
Construct the X-bar chart. Identify hours where
the process was out of control.
Transcribed Image Text:1.8 A Canadian manufacturer identified a critical diameter on a crank bore that needed to be maintained within a close tolerance for the product to be successful. Sam- ples of size 4 were taken every hour. The values of the differences (measurement - specification), in ten- thousandths of an inch, are given in Table 1.4. (a) Calculate the central line for an X-bar chart for the 24 hourly sample means. The centerline is x = — . . . (4.25 -3.00 -1.50 +3.25)/24. = (b) Is the average of all the numbers in the table, 4 for each hour, the same as the average of the 24 hourly averages? Should it be? (c) A computer calculation gives the control limits LCL = -4.48 UCL 7.88 = Construct the X-bar chart. Identify hours where the process was out of control.
Table 1.4 The differences (measurement
thousandths of an inch
2
3
Hour
I
10
Hour 13 14
5
9
=
6
6
8
10
-1
4
15
-5
4
-5
-2
5
-7
-2
-6
-8
5 2 5
3
1
-3 -3
-3
7
6
1
3
6
-4
0
9
1
3
1
10
-2
-3 -7
7 11
7 2 4
4
4.25 -3.00 -2.75 -5.00 -5.75 -3.75 -0.25 6.25 3.50 4.00 2.00 5.50
6
-14
7
-6 -1
-6
-1
-5 -2
-6
-1
2
-6
specification), in ten-
13
8
9 10 ||
16 17 18 19 20 21 22
-8
2 7
8
5
8 -5
-5
8
7
4 1
7
9
1
-4 5
6
7
0
1
7
0 1
3
6 10 -6 2
7.50 7.50 -2.00 -3.00 1.75 5.50 8.25 6.50 0.75 1.25 -1.50 3.25
12
8 -1
23 24
-2 -1
-4 5
-7
9
7
0
Transcribed Image Text:Table 1.4 The differences (measurement thousandths of an inch 2 3 Hour I 10 Hour 13 14 5 9 = 6 6 8 10 -1 4 15 -5 4 -5 -2 5 -7 -2 -6 -8 5 2 5 3 1 -3 -3 -3 7 6 1 3 6 -4 0 9 1 3 1 10 -2 -3 -7 7 11 7 2 4 4 4.25 -3.00 -2.75 -5.00 -5.75 -3.75 -0.25 6.25 3.50 4.00 2.00 5.50 6 -14 7 -6 -1 -6 -1 -5 -2 -6 -1 2 -6 specification), in ten- 13 8 9 10 || 16 17 18 19 20 21 22 -8 2 7 8 5 8 -5 -5 8 7 4 1 7 9 1 -4 5 6 7 0 1 7 0 1 3 6 10 -6 2 7.50 7.50 -2.00 -3.00 1.75 5.50 8.25 6.50 0.75 1.25 -1.50 3.25 12 8 -1 23 24 -2 -1 -4 5 -7 9 7 0
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