STAT 495, Fall 2003
Homework Assignment #6
You may use JMP, or other computer program, to construct the control charts asked for in this
assignment. When asked to calculate control limits, do so by hand and show your work.
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 number of defective chips in each subgroup is recorded below.
Subgroup
1
2
3
4
5
6
7
8
9
10
Number of
Defectives
4
2
6
2
7
3
3
4
2
8
Number of
Subgroup
11
12
13
14
15
16
17
18
19
20
Defectives
1
3
5
4
6
1
3
2
6
4
Number of
Subgroup
21
22
23
24
25
26
27
28
29
30
Defectives
5
4
4
2
6
10
4
5
2
4
(a) Construct a p-Chart from these data. Comment on the appearance of the chart and
note any subgroups that fall outside the control limits.
(b) Construct a np-Chart from these data. Comment on the appearance of the chart and
note any subgroups that fall outside the control limits. How does the np-Chart compare
to the p-Chart in (a)?
(c) One of the operators at the facility suggests using a new solvent to clean 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 below. Continue the p-Chart with the new
data, using the same limits as before.
(d) Comment on the appearance of the chart now. What can be said about the change that
was made?
(e) Construct a p-Chart based on the new data (subgroups 31-50) only. Compare the
centerline and control limits for the new chart with those in (a).
Subgroup
31
32
33
34
35
36
37
38
39
40
Number of
Defectives
3
0
3
2
2
1
2
4
0
2
Subgroup
41
42
43
44
45
46
47
48
49
50
Number of
Defectives
2
2
2
2
0
1
0
0
0
3
2. Ceramic boards for classrooms are produced in 4 foot by 8 foot sheets. The production
manager is concerned about the surface defects on the sheets. Below are the data.
Day
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Number
of Boards
1
5
2
3
2
2
3
1
1
3
4
3
3
4
Number
of Defects
2
5
3
8
1
4
8
0
2
8
5
7
4
6
Day
Number
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Number
of Boards
6
3
5
4
7
3
4
2
5
2
2
1
2
3
Number
of Defects
18
6
8
17
4
6
4
5
2
5
0
15
3
5
(a) Compute the average number of defects per day.
(b) Calculate the upper control limit (UCL) and lower control limit (LCL) for a c-Chart for
the number of defects. Construct the c-Chart.
(c) Are there any days that plot outside the control limits? If so, what days are they and
how many defects are there on those days?
(d) Another way to chart this data is with a U-Chart for the rate of defects per board.
Compute the average rate of defects per board.
(e) Because of the unequal number of boards inspected each day, the U-Chart will have
different limits for each day. Calculate the upper and lower control limits for day 15.
Construct the U-Chart.
(f) Looking at the U-Chart of surface defects on ceramic boards, are there any days that
plot outside the control limits? If so, what days are they and what is the rate of defects
on each of those days?
(g) Which chart, the c-Chart or the U-Chart gives a more accurate picture of the process
that is producing the ceramic boards? Explain briefly.