Q8) A manufacturer produces machine parts, and the diameter of the parts is monitored using an X-bar and R chart. The specification limits for the diameter are 55 and 45. A total of 20 samples, each consisting of 3 parts, were measured. The data for the sample averages (X-bar) and ranges (R) for the 20 samples are given below: Sample No. X-bar (mm) R (mm) 1 52 4 2 51 3 3 49 2 4 48 4 15 53 5 16 50 3 7 52 3 18 47 4 19 51 3 10 52 14 11 49 2 12 48 3 13 51 3 14 50 4 15 52 3 16 49 17 50 4 18 50 14 19 48 3 20 50 a) Calculate the overall average X-bar and average range (R bar)? (1 mark) b) Determine the trial control limits for the X-bar and R chart? (1 mark) c) Is the process out of control? Determine the mean and standard deviation of the above process? (1 mark) d) Assuming the diameter to be normally distributed, what proportion of product will not meet the specifications? (2 marks) e) Assume that the process mean shifts to 52 mm. Calculate the process fallout considering this mean shift? (2 marks)
Q8) A manufacturer produces machine parts, and the diameter of the parts is monitored using an X-bar and R chart. The specification limits for the diameter are 55 and 45. A total of 20 samples, each consisting of 3 parts, were measured. The data for the sample averages (X-bar) and ranges (R) for the 20 samples are given below: Sample No. X-bar (mm) R (mm) 1 52 4 2 51 3 3 49 2 4 48 4 15 53 5 16 50 3 7 52 3 18 47 4 19 51 3 10 52 14 11 49 2 12 48 3 13 51 3 14 50 4 15 52 3 16 49 17 50 4 18 50 14 19 48 3 20 50 a) Calculate the overall average X-bar and average range (R bar)? (1 mark) b) Determine the trial control limits for the X-bar and R chart? (1 mark) c) Is the process out of control? Determine the mean and standard deviation of the above process? (1 mark) d) Assuming the diameter to be normally distributed, what proportion of product will not meet the specifications? (2 marks) e) Assume that the process mean shifts to 52 mm. Calculate the process fallout considering this mean shift? (2 marks)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 27PFA
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Transcribed Image Text:Q8) A manufacturer produces machine parts, and the diameter of the
parts is monitored using an X-bar and R chart. The specification limits
for the diameter are 55 and 45. A total of 20 samples, each consisting of
3 parts, were measured. The data for the sample averages (X-bar) and
ranges (R) for the 20 samples are given below:
Sample No. X-bar (mm) R (mm)
1
52
4
2
51
3
3
49
2
4
48
4
15
53
5
16
50
3
7
52
3
18
47
4
19
51
3
10
52
14
11
49
2
12
48
3
13
51
3
14
50
4
15
52
3
16
49
17
50
4
18
50
14
19
48
3
20
50
a) Calculate the overall average X-bar and average range (R bar)? (1
mark)
b) Determine the trial control limits for the X-bar and R chart? (1
mark)
c) Is the process out of control? Determine the mean and standard
deviation of the above process? (1 mark)
d) Assuming the diameter to be normally distributed, what proportion
of product will not meet the specifications? (2 marks)
e) Assume that the process mean shifts to 52 mm. Calculate the
process fallout considering this mean shift? (2 marks)
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