Statistics 664 – Autumn 2010
Homework 7 Solutions
1.
Problem 6.7 (just redo part a of 6.2)
Here are the
x
and s charts from Minitab.
19
17
15
13
11
9
7
5
3
1
15.0
12.5
10.0
7.5
5.0
Sample
Sample Mean
_
_
X= 10.32
UCL= 14.73
LCL= 5.92
19
17
15
13
11
9
7
5
3
1
6.0
4.5
3.0
1.5
0.0
Sample
Sample StDev
_
S= 2.703
UCL= 6.125
LCL= 0
XbarS Chart of Ex62V
All points are within the control limits for both charts.
Thus the process appears to be in
control if we assume that the historical values for
x
and s represent “in control” values.
(Note: An acceptable alternative answer is the following.
The nominal output voltage is
supposed to be 350V.
This means that the x
i
values should fluctuate around 0, i.e., that
the center line in our
x
chart should be 0.
The upper and lower control limits would then
be LCL = 4.40 and UCL = 4.40.
Since all the points are above 5.77, every point would
be above the UCL and the process would be declared out of control).
2.
Problem 6.8 (just redo part a of 6.3)
Here are the
x
and s charts from Minitab.
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View Full Document19
17
15
13
11
9
7
5
3
1
40
20
0
20
Sample
Sample Mean
_
_
X= 10.9
UCL= 46.91
LCL= 25.11
19
17
15
13
11
9
7
5
3
1
60
45
30
15
0
Sample
Sample StDev
_
S= 25.23
UCL= 52.71
LCL= 0
XbarS Chart of Ex63Dia
All points in both charts are with the control limits so the process appears to be in control,
assuming the historical values represent “in control” values.
(Note: An alternative answer is to argue that if the process is in control the mean should
be 0.
This should be the center line of the
x
chart.
In this case, the control limits would
be LCL = –36.01 and UCL = 36.01. All the data lie within these control limits, but after
sample 7 all are positive, which would be considered unusual.
So one might argue that
the process is not in control after sample 7.)
3.
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 Spring '10
 BillNotz
 Statistics, Normal Distribution, Control Chart, LC L=

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