STAT 495, Fall 2010
Homework Assignment #6
1. A manufacturer of silicon chips has concerns about the number of defective chips
produced at one of its facilities. Subgroups of size n = 50 are taken at regular
intervals throughout one week’s production. The data on the number of defective
chips in each subgroup is recorded below.
Subgroup
1
2
3
4
5
6
7
8
9
10
Number
Defective
4
2
6
2
7
3
3
4
2
8
Subgroup
11
12
13
14
15
16
17
18
19
20
Number
Defective
1
3
5
4
6
1
3
2
6
4
Subgroup
21
22
23
24
25
26
27
28
29
30
Number
Defective
5
4
4
2
6
10
4
5
2
4
a) Calculate the average number defective for the 30 subgroups and use this to
compute the limits for an np control chart. Do these calculations by hand.
b) Use JMP to actually construct the np chart.
c) Compute the limits for a p control chart. Do these calculations by hand.
d) Use JMP to actually construct the p chart.
e) How does the p chart compare to the np chart?
f) Are there any subgroups that plot outside control limits on the p chart? If so,
which subgroups are they and what are the associated numbers of defective
chips?
g) If special causes are found for the subgroups identified in f) and those special
causes removed, how will the centerline and control limits change on the p
chart? You don’t have to calculate the new limits you simply have to say how
the centerline and limits will change and why?
h) One of the operators at the facility suggests using a different solvent for
cleaning the chips as the old solvent has impurities that may scratch the
surface. After the solvent is changed, more data are collected. These data
appear on the next page.
Construct a “standards given” p chart.
Use p = 0.07793 , the average fraction defective if subgroups in f) are
removed, to chart both the old data and the new data.
i) Comment on the appearance of the chart now. What can be said about the
change that was made?
j) Construct a p chart based on the new data only (subgroups 31 through 50).
Compare the centerline and control limits for the new chart with those in h).
1
Subgroup
31
32
33
34
35
36
37
38
39
40
Number
Defective
3
0
3
2
2
1
2
4
0
2
Subgroup
41
42
43
44
45
46
47
48
49
50
Number
Defective
2
2
2
2
2
1
0
0
0
3
2. At an automobile assembly plant, body sides are attached to the underbody at a
particular assembly station. A fault (defective car) occurs whenever both body
sides are unable to be placed on the car properly. Below are the number of cars
built and the number of faults for each of 50 day’s production. Of the 24,317 cars
built there are 1,652 faults (defective cars). The data is also available on WebCT
and the course web page.
Data on Cars produced and Faults (Defective Cars)
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Cars
484
445
482
476
511
504
535
517
453
479
514
509
443
453
494
512
422
Faults
43
44
33
42
43
47
33
51
18
38
28
17
24
29
38
28
21
Day
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Cars
406
477
497
522
516
470
441
504
506
477
468
470
486
518
500
469
507
Faults
30
25
45
13
21
34
21
32
31
31
49
36
26
36
30
52
33
Day
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Cars
530
517
497
478
426
453
495
474
530
506
489
496
501
474
497
487
Faults
26
26
25
34
34
28
30
45
42
35
31
28
13
59
43
31
a) What are the center line and control limits for the p control chart for Day 1?
b) Use JMP to construct the p control chart.
c) Are there any days that plot outside the control limits? If so, what days are
they and what are the associated fractions defective?
d) If special causes are found for the days that plot outside the control limits
would you want to eliminate those special causes? Explain briefly.
2
3. Ceramic boards for use in classrooms are produced in 4 foot by 9 foot sheets. The
production manager is concerned about the surface defects i.e. scratches, off-color
spots, dents, etc. on the sheets. Below are the data.
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Number Number Day
of
of
Boards Defects
1
2
15
5
5
16
2
3
17
3
8
18
2
1
19
2
4
20
3
8
21
1
0
22
1
2
23
3
8
24
4
5
25
3
7
26
3
4
27
4
6
28
Number Number
of
of
Boards Defects
6
18
3
6
5
8
4
17
7
4
3
6
4
4
2
5
5
2
2
5
2
0
1
15
2
3
3
5
a) Compute the average number of defects per day?
b) Calculate by hand the upper and lower control limits for a c chart for the
number of defects per day.
c) Use JMP to construct the c control chart for the number of defects per day.
d) Are there any days that plot outside control limits on the c chart? If so, what
days are they and how defects were there on those days?
e) Another way to chart these data is with a U chart for the rate of defects per
board. Compute the average rate of defects per board.
f) Compute the control limits by hand for the rate of defects per board for day 1.
g) Use JMP to construct the U control chart for the rate of defects per board.
h) Are there any days that plot outside control limits on the U chart? If so, what
days are they and what is the rate of defects per board on each of those days.
i) Which chart, the c chart or U chart gives a more informative picture of the
process that is producing the ceramic boards? Explain briefly.
3