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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.

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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 22SGR
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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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