Frozen orange juice concentrate is packed in 6-oz cardboard cans.
These cans are formed on a machine by
spinning them from cardboard stock and attaching a metal bottom panel. By inspection of a can, we may
determine whether, when filled, it could possibly leak either on the side seam or around the bottom joint.
Such a nonconforming can has an improper seal on either the side seam or the bottom panel. Set up a
control chart to improve the fraction of nonconforming cans produced by this machine. n=50
Nunber of
Sample 0.6
Nonconfo N P UCL P-bar LCL
Number
rming
0.5
1 12 50 0.24 0.410239 0.231333 0.052428
2 15 50 0.3 0.410239 0.231333 0.052428
3 8 50 0.16 0.410239 0.231333 0.052428 0.4
4 10 50 0.2 0.410239 0.231333 0.052428
5 4 50 0.08 0.410239 0.231333 0.052428 0.3
6 7 50 0.14 0.410239 0.231333 0.052428
7 16 50 0.32 0.410239 0.231333 0.052428 0.2
8 9 50 0.18 0.410239 0.231333 0.052428
9 14 50 0.28 0.410239 0.231333 0.052428 0.1
10 10 50 0.2 0.410239 0.231333 0.052428
11 5 50 0.1 0.410239 0.231333 0.052428
0
12 6 50 0.12 0.410239 0.231333 0.052428 1 2 3 4 5 6 7
13 17 50 0.34 0.410239 0.231333 0.052428
14 12 50 0.24 0.410239 0.231333 0.052428
15 22 50 0.44 0.410239 0.231333 0.052428
16 8 50 0.16 0.410239 0.231333 0.052428
17 10 50 0.2 0.410239 0.231333 0.052428
18 5 50 0.1 0.410239 0.231333 0.052428
19 13 50 0.26 0.410239 0.231333 0.052428
20 11 50 0.22 0.410239 0.231333 0.052428
21 20 50 0.4 0.410239 0.231333 0.052428
22 18 50 0.36 0.410239 0.231333 0.052428
23 24 50 0.48 0.410239 0.231333 0.052428
24 15 50 0.3 0.410239 0.231333 0.052428
25 9 50 0.18 0.410239 0.231333 0.052428
26 12 50 0.24 0.410239 0.231333 0.052428
27 7 50 0.14 0.410239 0.231333 0.052428
28 13 50 0.26 0.410239 0.231333 0.052428
29 9 50 0.18 0.410239 0.231333 0.052428
30 6 50 0.12 0.410239 0.231333 0.052428
P Chart
0.6
0.5
0.4
0.3
0.2
0.1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
P UCL P-bar LCL
Sample Sample Nunber of
P0 CL=np0 UCL LCL
Number Size Nonconforming
1 100 12 0.09551 9.55102 18.36857 0.733469
2 80 8 0.09551 7.640816 15.52747 -0.245841
3 80 6 0.09551 7.640816 15.52747 -0.245841
4 100 9 0.09551 9.55102 18.36857 0.733469
5 110 10 0.09551 10.50612 19.75405 1.258197 np
6 110 12 0.09551 10.50612 19.75405 1.258197
25
7 100 11 0.09551 9.55102 18.36857 0.733469
8 100 16 0.09551 9.55102 18.36857 0.733469
20
9 90 10 0.09551 8.595918 16.96098 0.230855
10 90 6 0.09551 8.595918 16.96098 0.230855
11 110 20 0.09551 10.50612 19.75405 1.258197
15
12 120 15 0.09551 11.46122 21.12037 1.802081
13 120 9 0.09551 11.46122 21.12037 1.802081
10
14 120 8 0.09551 11.46122 21.12037 1.802081
15 110 6 0.09551 10.50612 19.75405 1.258197
5
16 80 8 0.09551 7.640816 15.52747 -0.245841
17 80 10 0.09551 7.640816 15.52747 -0.245841
18 80 7 0.09551 7.640816 0
15.52747 -0.245841
1 2 3 4 5 6 7 8 9 10 11 12
19 90 5 0.09551 8.595918 16.96098 0.230855
20 100 8 0.09551 9.55102 18.36857 0.733469
-5
21 100 5 0.09551 9.55102 18.36857 0.733469
Nunber of
22 100 8 0.09551 9.55102 18.36857 0.733469 Nonconforming
23 100 10 0.09551 9.55102 18.36857 0.733469
24 90 6 0.09551 8.595918 16.96098 0.230855
25 90 9 0.09551 8.595918 16.96098 0.230855
np Chart
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Nunber of CL=np0 UCL LCL
Nonconforming
Table presents the number of nonconformities observed in 26 successive samples of 100 printed circuit boards. Note that, for
c chart for these data.
Nunber of
Sample Nonconfo UCL C-bar LCL
Number C Ch
rmities
45
1 21 33.21086 19.84615 6.481447
2 24 33.21086 19.84615 6.481447 40
3 16 33.21086 19.84615 6.481447
35
4 12 33.21086 19.84615 6.481447
5 15 33.21086 19.84615 6.481447 30
6 5 33.21086 19.84615 6.481447 25
7 28 33.21086 19.84615 6.481447
8 20 33.21086 19.84615 6.481447 20
9 31 33.21086 19.84615 6.481447 15
10 25 33.21086 19.84615 6.481447
10
11 20 33.21086 19.84615 6.481447
12 24 33.21086 19.84615 6.481447 5
13 16 33.21086 19.84615 6.481447
0
14 19 33.21086 19.84615 6.481447 1 2 3 4 5 6 7 8 9 10 11 12 13
15 10 33.21086 19.84615 6.481447
Nunber of
16 17 33.21086 19.84615 6.481447 Nonconformities
17 13 33.21086 19.84615 6.481447
18 22 33.21086 19.84615 6.481447
19 18 33.21086 19.84615 6.481447
20 39 33.21086 19.84615 6.481447
21 30 33.21086 19.84615 6.481447
22 24 33.21086 19.84615 6.481447
23 16 33.21086 19.84615 6.481447
24 19 33.21086 19.84615 6.481447
25 17 33.21086 19.84615 6.481447
26 15 33.21086 19.84615 6.481447
d circuit boards. Note that, for reasons of convenience, the inspection unit is defined as 100 boards. Set up a
rt for these data.
C Chart
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Nunber of UCL C-bar LCL
Nonconformities
A supply chain engineering group monitors shipments of materials through the company distribution
network. Errors on either the delivered material or the accompanying documentation are tracked on a
weekly basis. Each week 50 randomly selected shipments are examined and the errors recorded. Data for
twenty weeks are shown in Table 7.10. Set up a u control chart to monitor this process.
Total 0.25
Sample Nuber of
Number Sample Errors U UCL U-Bar = CL LCL
Size 0.2
(week) (Nonconf
ormities)
0.15
1 50 2 0.04 0.189412 0.074 -0.041412
2 50 3 0.06 0.189412 0.074 -0.041412 0.1
3 50 8 0.16 0.189412 0.074 -0.041412
4 50 1 0.02 0.189412 0.074 -0.041412 0.05
5 50 1 0.02 0.189412 0.074 -0.041412
6 50 4 0.08 0.189412 0.074 -0.041412
0
7 50 1 0.02 0.189412 0.074 -0.041412 1 2 3 4 5 6 7
8 50 4 0.08 0.189412 0.074 -0.041412
-0.05
9 50 5 0.1 0.189412 0.074 -0.041412
10 50 1 0.02 0.189412 0.074 -0.041412
-0.1
11 50 8 0.16 0.189412 0.074 -0.041412
12 50 2 0.04 0.189412 0.074 -0.041412 U
13 50 4 0.08 0.189412 0.074 -0.041412
14 50 3 0.06 0.189412 0.074 -0.041412
15 50 4 0.08 0.189412 0.074 -0.041412
16 50 1 0.02 0.189412 0.074 -0.041412
17 50 8 0.16 0.189412 0.074 -0.041412
18 50 3 0.06 0.189412 0.074 -0.041412
19 50 7 0.14 0.189412 0.074 -0.041412
20 50 4 0.08 0.189412 0.074 -0.041412
U Chart
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
U UCL U-Bar = CL LCL
