Mgt 2070 Assignment 4 – Solutions
6.5
Use Pareto analysis to investigate the following data collected on a printed-circuit-board
assembly line.
Defect
Wrong component
Components not adhering
Excess adhesive
Misplaced transistors
Defective board dimension
Mounting holes improperly positioned
Circuitry problems on final test
Number of Defect Occurrences
217
146
64
600
143
14
92
a) Prepare a graph of the data (5 marks)
1400
1200
1000
800
Defects
Cum %
600
400
200
H
ol
es
ss
Ex
ce
y
ui
tr
C
irc
io
n
en
s
D
im
Ad
he
re
po
ne
nt
C
om
Tr
an
s
is
t
or
s
0
b) What conclusions do you reach? (5 marks)
Most of the errors are the result of misplaced transistors. This is the problem the company should
concentrate on first.
S6.3 The overall average of a process you are attempting to monitor is 50 units. The average
range is 4 units. The sample size you are using is n = 5.
a) What are the upper and lower control limits of the appropriate mean charts? (5 marks)
b) What are the upper and lower control limits of the appropriate range chart?
From table S6.1 where n = 5, we have A2 = 0.577, D4 = 2.115, and D3 = 0.
UCL X  X  A 2  R  50  0.577  4  52.308
LCL X  X  A 2  R  50  0.577  4  47.692
UCL R  D 4  R  2.115  4  8.456
LCL R  D3  R  0  4  0
S6.7 Pet Products Inc. caters to the growing market for cat supplies, with a full line of
products ranging from litter to toys to flea powder. One of its newer products, a tube of fluid that
prevents hairballs in long-haired cats, is produced by an automated machine set to fill each tube
with 63.5 grams of paste.
To keep this filling process under control, four tubes are pulled randomly from the
assembly line every 4 hours. After several days, the data shown in the table that follows resulted.
Set control limits for this process and graph the sample data for both the x- and R-charts. Is the
process in control?
x
R
x
R
1
63.5
2.0
14
63.3
1.5
2
63.6
1.0
15
63.4
1.7
3
63.7
1.7
4
63.9
0.9
16
63.4
1.4
17
63.5
1.1
Sample Number
5
6
7
8
63.4 63.0 63.2 63.3
1.2
1.6
1.8
1.3
Sample Number
18
19
20
63.6 63.8 63.5
1.8
1.3
1.6
9
63.7
1.6
21
63.9
1.0
10
63.5
1.3
22
63.2
1.8
11
63.3
1.8
23
63.3
1.7
12
63.2
1.0
24
64.0
2.0
13
63.6
1.8
25
63.4
1.5
X  63.49, R  1.5, n  4. From table S6.1 where n = 4, we have A2 = 0.729, D4 = 2.282, and
D3 = 0.
UCL X  X  A 2  R  63.49  0.729  1.5  64.58
LCL X  X  A 2  R  63.49  0.729  1.5  62.40
UCL R  D 4  R  2.282  1.5  3.423
LCL R  D3  R  0  1.5  0
(4 marks)
Adjustable weight in grams
X-bar Control Chart (2 marks)
65
64.5
64
63.5
63
62.5
62
61.5
61
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
Sample
Average range in grams
R Control Chart (2 marks)
4
3.5
3
2.5
2
1.5
1
0.5
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
Sample
The x-bar and range charts both show that the process is in control. (2 marks)
S6.19 The smallest defect in a computer chip will render the entire chip worthless. Therefore,
tight quality control measures must be established to monitor these chips. In the past, the
percentage defective at a California-based company has been 1.1%. The sample size is 1,000.
Determine upper and lower control chart limits for these computer chips. Use z = 3.
In a sample size of 1,000, the mean fraction defective in the sample (p-hat) is 0.011 (ie 1.1%).
UCL pˆ  p  z pˆ  p  z
p(1 - p)
0.011(0.989)
 0.011  3
 0.0209
n
1000
p(1 - p)
0.011(0.989)
LCL pˆ  p  z pˆ  p  z
 0.011  3
 0.0011
n
1000
(10 marks)