For the sample data provided in Problem 3-14, construct an r-chart in conjunctio
ID: 1138836 • Letter: F
Question
For the sample data provided in Problem 3-14, construct an r-chart in conjunction with the R-chart, plot the sample observations, and, using both i- and R-charts, comment on the process control. Samples Tempera turelF 46.348.1 425 43.1 396 1.2 40.5 37.8 36.5 42.3 40.1 413 345 33.2 36 42.3 .1 39.5 37.7 38.6 35.2 38.140.5 39.1 423 40.6 417 38.6 435 44 33.2 38.6 41.5 40.7 43.1 41.8 40.0 41.6 44.7 393 42.4 41.6 40.840.942.3 44.7 365 37.3 35.3 41. 42.6 435 35.4 36.1 38.2 40.5 404 39.1 37.2 41. 45.3 42.0 43.1 7 395 36.4 37.5 26,2 30,9 40,1 40.5 343 36.2 35.1 368 39.5 38.2 37.6 341 387 37.6 40.6 40.3 39.7 41 41.0 343 39.1 452 437 40.9 42.3 37.6 354 34 37.6 392 39.3 41.2 37 12 13 14 17 19 20Explanation / Answer
Solution:
Samples
Temperature (F)
x
R
1
46.30
48.10
42.50
43.10
39.60
43.92
8.50
2
41.20
40.50
37.80
36.50
42.30
39.66
5.80
3
40.10
41.30
34.50
33.20
36.70
37.16
8.10
4
42.30
44.10
39.50
37.70
38.60
40.44
6.40
5
35.20
38.10
40.50
39.10
42.30
39.04
7.10
6
40.60
41.70
38.60
43.50
44.60
41.80
6.00
7
33.20
38.60
41.50
40.70
43.10
39.42
9.90
8
41.80
40.00
41.60
40.70
39.30
40.68
2.50
9
42.40
41.60
40.80
40.90
42.30
41.60
1.60
10
44.70
36.50
37.30
35.30
41.10
38.98
9.40
11
42.60
43.50
35.40
36.10
38.20
39.16
8.10
12
40.50
40.40
39.10
37.20
41.60
39.76
4.40
13
45.30
42.00
43.10
44.70
39.50
42.92
5.80
14
36.40
37.50
36.20
38.90
40.10
37.82
3.90
15
40.50
34.30
36.20
35.10
36.80
36.58
6.20
16
39.50
38.20
37.60
34.10
38.70
37.62
5.40
17
37.60
40.60
40.30
39.70
41.20
39.88
3.60
18
41.00
34.30
39.10
45.20
43.70
40.66
10.90
19
40.90
42.30
37.60
35.40
34.80
38.20
7.50
20
37.60
39.20
39.30
41.20
37.60
38.98
3.60
TOTAL
794.28
124.7
Working:
R = 124.7 / 20 = 6.235
x = 794.28 / 20 = 39.714
UCL = D4 R = 2.11 * 6.235 = 13.1559
LCL = D3 R = 0 * 6.235 = 0
UCL = x + A2 R = 39.714 + (0.58 * 6.235) = 43.3303
LCL = x - A2 R = 39.714 - (0.58 * 6.235) = 36.0977
The usage of x-chart and R-chart indicates that the process is out of control because the point of sample 1 in x-chart although it is inside the control limit in R-chart but is above the upper control limit. The x-chart and R-chart need to be together to know whether the process in control or not as the two charts measure the process in differently. In the current scenario all the point of sample in R-chart lies between the control limit line. However while using a x-chart, it reflects that point of sample 1 is above the upper control limit. Thus we can conclude that this occurrence indicate that this process is out of control.
Samples
Temperature (F)
x
R
1
46.30
48.10
42.50
43.10
39.60
43.92
8.50
2
41.20
40.50
37.80
36.50
42.30
39.66
5.80
3
40.10
41.30
34.50
33.20
36.70
37.16
8.10
4
42.30
44.10
39.50
37.70
38.60
40.44
6.40
5
35.20
38.10
40.50
39.10
42.30
39.04
7.10
6
40.60
41.70
38.60
43.50
44.60
41.80
6.00
7
33.20
38.60
41.50
40.70
43.10
39.42
9.90
8
41.80
40.00
41.60
40.70
39.30
40.68
2.50
9
42.40
41.60
40.80
40.90
42.30
41.60
1.60
10
44.70
36.50
37.30
35.30
41.10
38.98
9.40
11
42.60
43.50
35.40
36.10
38.20
39.16
8.10
12
40.50
40.40
39.10
37.20
41.60
39.76
4.40
13
45.30
42.00
43.10
44.70
39.50
42.92
5.80
14
36.40
37.50
36.20
38.90
40.10
37.82
3.90
15
40.50
34.30
36.20
35.10
36.80
36.58
6.20
16
39.50
38.20
37.60
34.10
38.70
37.62
5.40
17
37.60
40.60
40.30
39.70
41.20
39.88
3.60
18
41.00
34.30
39.10
45.20
43.70
40.66
10.90
19
40.90
42.30
37.60
35.40
34.80
38.20
7.50
20
37.60
39.20
39.30
41.20
37.60
38.98
3.60
TOTAL
794.28
124.7
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