4D. Articles are mass-produced to a specified width of 0-15 cm. In order to check that the production process is running satisfactorily, random samples of five articles are taken at regular time intervals, and the widths measured. The following are the means and ranges of the widths in 20 consecutive samples, where the widths are measured from the specified value in units of 0.0001 cm. Sample Sample Sample number mean range Sample Sample Sample number mean range 1 1-0 32 11 -1.6 18 2 2.4 21 12 -2.2 14 3 -2.4 19 13 1.6 6 4 3.2 6 14 0-4 15 1-4 11 15 2-0 18 6 1.2 17 16 3-0 16 7 2-6 13 17 1-6 18 8 0-4 9 18 -7-6 11 9 -2.2 14 19 <-5-4 15 10 -3.8 8 20 -4-2 8 Using these results, convert the average range into an estimate of the standard deviation of the widths of the articles in the population of manufactured articles. (If the range of a random sample of size 5 from a normal population is r, then an estimate of the standard deviation is given by multiplying r by 0-4299.) Hence draw a control chart for means, showing both 2-5% control limits (warning limits) and 0-1% control limits (action limits). Describe how this chart could be used to determine whether or not the manufacturing process is under control. What would your conclusion be for the data provided?
4D. Articles are mass-produced to a specified width of 0-15 cm. In order to check that the production process is running satisfactorily, random samples of five articles are taken at regular time intervals, and the widths measured. The following are the means and ranges of the widths in 20 consecutive samples, where the widths are measured from the specified value in units of 0.0001 cm. Sample Sample Sample number mean range Sample Sample Sample number mean range 1 1-0 32 11 -1.6 18 2 2.4 21 12 -2.2 14 3 -2.4 19 13 1.6 6 4 3.2 6 14 0-4 15 1-4 11 15 2-0 18 6 1.2 17 16 3-0 16 7 2-6 13 17 1-6 18 8 0-4 9 18 -7-6 11 9 -2.2 14 19 <-5-4 15 10 -3.8 8 20 -4-2 8 Using these results, convert the average range into an estimate of the standard deviation of the widths of the articles in the population of manufactured articles. (If the range of a random sample of size 5 from a normal population is r, then an estimate of the standard deviation is given by multiplying r by 0-4299.) Hence draw a control chart for means, showing both 2-5% control limits (warning limits) and 0-1% control limits (action limits). Describe how this chart could be used to determine whether or not the manufacturing process is under control. What would your conclusion be for the data provided?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:4D.
Articles are mass-produced to a specified width of 0-15 cm. In order to check that the
production process is running satisfactorily, random samples of five articles are taken at regular
time intervals, and the widths measured. The following are the means and ranges of the widths
in 20 consecutive samples, where the widths are measured from the specified value in units of
0.0001 cm.
Sample Sample Sample
number
range
Sample Sample Sample
number
mean
mean
range
1
1.0
32
11
-1.6
18
2
2.4
21
12
-2.2
14
3
-2.4
19
13
1.6
6
4
3.2
6
14
0.4
15
5
1.4
11
15
2.0
18
6
1.2
17
16
3-0
16
7
2.6
13
17
1-6
18
8
0-4
9
18
-7.6
11
9
-2.2
14
19
-5.4
15
10
-3.8
8
20
-4.2
8
Using these results, convert the average range into an estimate of the standard deviation of the
widths of the articles in the population of manufactured articles. (If the range of a random
sample of size 5 from a normal population is r, then an estimate of the standard deviation is
given by multiplying r by 0-4299.)
Hence draw a control chart for means, showing both 2-5% control limits (warning limits) and
0.1% control limits (action limits). Describe how this chart could be used to determine whether
or not the manufacturing process is under control. What would your conclusion be for the data
provided?
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