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220
Chapter 18: Statistical Applications in Quality and Productivity Management
CHAPTER 17
17.1
(a)
Proportion of nonconformances largest on Day 5, smallest on Day 3.
0
0.1
0.2
0.3
0
2
4
6
8
10
Day
Proportion
(b)
n
= 100,
p
= 1.48/10 = 0.148,
04147
.
0
100
)
148
.
0
1
(
148
.
0
3
148
.
0
)
1
(
3
=


=


=
n
p
p
p
LCL
,
25453
.
0
100
)
148
.
0
1
(
148
.
0
3
148
.
0
)
1
(
3
=

+
=

+
=
n
p
p
p
UCL
(c)
Proportions are within control limits, so there does not appear to be any special
causes of variation.
17.2
(a)
Proportion of nonconformances largest on Day 4, smallest on Day 3.
0
0.1
0.2
0.3
0
2
4
6
8
10
Day
(b)
n
= 1036/10 = 103.6,
p
= 148/1036 = 0.142857,
(1
)
0.142857(1 0.142857)
3
0.142857
3
0.039719
103.6
p
p
LCL
p
n


=

=

=
(1
)
0.142857(1 0.142857)
3
0.142857
3
0.245995
103.6
p
p
UCL
p
n


=
+
=
+
=
(c)
Proportions are within control limits, so there do not appear to be any special causes
of variation.
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Chapter 18: Statistical Applications in Quality and Productivity Management
17.3
(a)
n
= 235,
p
= 538/4700 = 0.1145,
0522
.
0
235
)
1145
.
0
1
(
1145
.
0
3
1145
.
0
)
1
(
3
=


=


=
n
p
p
p
LCL
,
1768
.
0
235
)
1145
.
0
1
(
1145
.
0
3
1145
.
0
)
1
(
3
=

+
=

+
=
n
p
p
p
UCL
0
0.05
0.1
0.15
0.2
0.25
0.3
0
5
10
15
20
Day
Proportion
The proportion of late arrivals on Day 13 is substantially out of control. Possible
causes of this value should be investigated. In addition, the next four highest points
all occur on a Friday.
(b)
The snowstorm would explain why the proportion of late arrivals was so high on Day
13.
(c)
The results would have been the same. The proportion of late arrivals on Day 13
would still have been above the
UCL
.
17.4
(a)
(b)
Although none of the points are outside the control limits, there is
evidence of a pattern over time, since the first eight points are all below the center
line and most of the later points are above the center line. Thus, the special causes
that might be contributing to this pattern should be investigated before any change in
the system of operation is contemplated.
Solutions to EndofSection and Chapter Review Problems
222
17.5
(a)
n
= 102.5667,
p
= 0.308742,
LCL
= 0.171895,
UCL
= 0.44559
Note: The UCL and LCL are represented by jagged lines which are the control limits
for each day depending on the sample size of that day.
(b)
Yes, the process gives an out of control signal because the proportions fall outside of
the control limits on four of the 30 days.
(c)
n
= 103.1923,
p
= 0.297428,
LCL
= 0.162428,
UCL
= 0.432428
Control Chart: Records not Processed
Sigma level: 3
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
Proportion Nonconforming
.6
.5
.4
.3
.2
.1
0.0
Records not Processe
d
UCL
Center = .31
LCL
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Chapter 18: Statistical Applications in Quality and Productivity Management
17.6
(a)
n
= 113345/22 = 5152.0455,
p
= 1460/113345 = 0.01288,
00817
.
0
0455
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This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue University.
 Spring '08
 Harris

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