Question 1: A manufacturer of wood screws periodically examines screws heads for the presence or absence of burrs. Subgroups of 300 screws are selected and examined using a carefully designed procedure. The collected data is as follows:
|
Observation
|
Number of Screws with Burrs
|
|
1
|
19
|
|
2
|
16
|
|
3
|
11
|
|
4
|
6
|
|
5
|
22
|
|
6
|
2
|
|
7
|
4
|
|
8
|
7
|
|
9
|
5
|
|
10
|
27
|
|
11
|
7
|
|
12
|
13
|
|
13
|
17
|
|
14
|
29
|
|
15
|
1
|
|
16
|
2
|
|
17
|
19
|
|
18
|
28
|
|
19
|
24
|
|
20
|
23
|
a- Find the centerline (show your calculations)
b- Find the control limits (show your calculations)
c- Use MINITAB to develop the appropriate control chart
d- Are there any special causes of variation? Which observations?
e- What to do next?
Question 2: A given model of large radar dish represents the area of opportunity in which nonconformities may occur. Results of quality check for 25 radar assemblies are as follows:
|
Radar Assembly Number
|
Number of Nonconformities
|
|
1
|
25
|
|
2
|
60
|
|
3
|
28
|
|
4
|
65
|
|
5
|
91
|
|
6
|
56
|
|
7
|
40
|
|
8
|
54
|
|
9
|
90
|
|
10
|
44
|
|
11
|
62
|
|
12
|
81
|
|
13
|
70
|
|
14
|
75
|
|
15
|
24
|
|
16
|
50
|
|
17
|
70
|
|
18
|
56
|
|
19
|
21
|
|
20
|
88
|
|
21
|
34
|
|
22
|
82
|
|
23
|
53
|
|
24
|
102
|
|
25
|
64
|
a- Determine the centerline (show your calculations)
b- Determine the control limits (show your calculations)
c- Use MINITAB to develop the appropriate control chart
d- Are there any indications of lack of control?
e- What to do next?
Question 3: Workers at a packaging operation shovels a granular product from a large pile into sacks that are then sealed and placed on pallets for shipping. A sequence of 25 subgroups each consisting of the weights of 5 sacks has been recorded as follows:
|
|
Observations
|
|
Subgroup #
|
Sack 1
|
Sack 2
|
Sack 3
|
Sack 4
|
Sack 5
|
|
1
|
35.4
|
35.6
|
34.8
|
34.7
|
34.8
|
|
2
|
36
|
35.6
|
34.9
|
34.8
|
35.9
|
|
3
|
35.2
|
35
|
35
|
35.4
|
35.1
|
|
4
|
34.8
|
35.8
|
35.2
|
35
|
34.9
|
|
5
|
34.2
|
35
|
36.1
|
34.9
|
35.1
|
|
6
|
36
|
35
|
35.2
|
34.8
|
34.9
|
|
7
|
36.1
|
34.9
|
34.5
|
35
|
35.1
|
|
8
|
35.1
|
35
|
35.6
|
34.9
|
36.2
|
|
9
|
35
|
35.6
|
36.1
|
34.8
|
35.6
|
|
10
|
35.4
|
35.8
|
36
|
34.2
|
36
|
|
11
|
35.2
|
35.3
|
35.2
|
35.9
|
34.8
|
|
12
|
35.9
|
36
|
35.1
|
35.1
|
35.6
|
|
13
|
35.2
|
35.6
|
35
|
34.9
|
35
|
|
14
|
35.2
|
35.6
|
35.8
|
35
|
35.1
|
|
15
|
34.9
|
34.8
|
35
|
35.2
|
34.9
|
|
16
|
35.2
|
35.3
|
35.2
|
35.6
|
35.1
|
|
17
|
35.6
|
35.8
|
35.2
|
35.4
|
34.9
|
|
18
|
35.2
|
35.6
|
35.4
|
35.6
|
35.2
|
|
19
|
34.7
|
34.9
|
35.6
|
35.2
|
35
|
|
20
|
35
|
35.1
|
35.6
|
35
|
35.1
|
|
21
|
35.6
|
35
|
35.8
|
35.2
|
34.6
|
|
22
|
34.9
|
35.1
|
35.6
|
35
|
35.2
|
|
23
|
35.9
|
36
|
35.2
|
36
|
35.2
|
|
24
|
35.2
|
35.1
|
35.4
|
34.9
|
35.1
|
|
25
|
35.2
|
35.2
|
35.1
|
35.6
|
34.9
|
a- What is the appropriate control chart that can be used by the quality engineer in this case?
b- Determine the control limits (show your calculations)
c- Construct the appropriate control chart for the data above using MINITAB.
d- Is the process in-control? If not, when does the out-of-control behavior occur?
e- If the process is found to be out of control, drop the out-of-control points and use MINITAB to re-construct the control chart.
f- Is the process now in-control? If not, what to do next?
Question 4: Viscosity is one of the important quality characteristics of paste ink used in printing presses. A viscosity measure is taken at the end of production of each batch of ink. Viscosity measures for 50 consecutive batches have been recorded as follows:
|
Sample
|
Viscosity
|
|
|
Sample
|
Viscosity
|
|
1
|
305
|
|
|
26
|
291
|
|
2
|
274
|
|
|
27
|
301
|
|
3
|
290
|
|
|
28
|
290
|
|
4
|
314
|
|
|
29
|
290
|
|
5
|
291
|
|
|
30
|
308
|
|
6
|
315
|
|
|
31
|
306
|
|
7
|
301
|
|
|
32
|
292
|
|
8
|
298
|
|
|
33
|
279
|
|
9
|
306
|
|
|
34
|
276
|
|
10
|
305
|
|
|
35
|
285
|
|
11
|
270
|
|
|
36
|
296
|
|
12
|
296
|
|
|
37
|
275
|
|
13
|
307
|
|
|
38
|
299
|
|
14
|
284
|
|
|
39
|
301
|
|
15
|
280
|
|
|
40
|
294
|
|
16
|
264
|
|
|
41
|
312
|
|
17
|
299
|
|
|
42
|
289
|
|
18
|
270
|
|
|
43
|
278
|
|
19
|
275
|
|
|
44
|
288
|
|
20
|
276
|
|
|
45
|
299
|
|
21
|
294
|
|
|
46
|
270
|
|
22
|
313
|
|
|
47
|
308
|
|
23
|
304
|
|
|
48
|
298
|
|
24
|
310
|
|
|
49
|
294
|
|
25
|
271
|
|
|
50
|
306
|
a- What is the appropriate control chart that can be used by the quality engineer in this case?
b- Determine the control limits (show your calculations)
c- Construct the appropriate control chart for the data above using MINITAB.
d- Is the process in-control? If not, when does the out-of-control behavior occur?
e- If the process is found to be out of control, drop the out-of-control points and use MINITAB to re-construct the control chart.
f- Is the process now in-control? If not, what to do next?