chapter 3: quality management1 solutions to chapter 3 exercises
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Chapter 3: Quality Management 1
Solutions to Chapter 3 Exercises
Chapter 3: Quality Management 2
Exercise 1
195
98
87
52
43
29
0
20
40
60
80
100
120
140
160
180
200
Number of Errors
Spelling Tense change Incompletesentences
Capitalization Punctuation Subject-verbagreement
Error Category
Pareto Chart
Chapter 3: Quality Management 3
Exercise 2Runs Chart
0
2
4
6
8
10
12
14
16
18
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month
Nu
mb
er
of
Can
cellati
on
s
Chapter 3: Quality Management 4
Exercise 2 continued
The upward trend in cancellations and non-renewals is a definite cause for concern.
Chapter 3: Quality Management 5
Exercise 3
limits control are $128,260 to$75,740 Or,
.7574 ).308(.8526 - 1.02 LCL
1.2826 ).308(.8526 1.02 UCL
10 of sizes samplefor 308.A
8526.R
02.16
12.6X
2
Chapter 3: Quality Management 6
Exercise 3 concluded
Jun Jul Aug Sep Oct Nov
1.2826
1.02
.7574
UCL
LCL
**
*
* *
*
Chapter 3: Quality Management 7
Exercise 4
Xi
3,500
4,100
3,750
4,300
4,000
3,650
Total 23,300
4270 .483(800) 3883.3 UCL
3497 .483(800) - 3883.3 LCL
6 of size sample afor 483.0A
800 3500 - 4300R
3.883,36/300,23X
2
Chapter 3: Quality Management 8
Exercise 5
0
10
20
30
40
50
60
70
1 2 3 4 5 6 7 8 9 10 11 12
Data
Mean
UCL
LCL
Chapter 3: Quality Management 9
Exercise 5 concluded
Normally control limits are set at three sigma so any point outside the limits is to be investigated. For limits set at lower sigma values, it should be considered that there is a chance of a random point falling outside the limits even though the process is in control. For one-sigma limits the chance is 32% or one out of three points. For two-sigma limits the chance is 5%, or one point out of twenty. In our case there are 3 points out of twelve, so action should be taken, but if these had been one-sigma limits, action would be unnecessary.
Chapter 3: Quality Management 10
Exercise 6a
Day Range
Sat 3
Sun 4
Mon 2
Tue 5
Wed 3
Thu 5
Sum 22
0 3.67(0) LCL
9.45 )3.67(2.575 UCL
0D ;575.2D
67.36/22R
34
For Friday the range is 7, so the range on Friday is in control.
Chapter 3: Quality Management 11
Exercise 6a concluded
9.45
3.67
0
Sat Sun Mon Tue Wed Thu Fri
UCL
LCL*
*
*
*
*
*
*
Chapter 3: Quality Management 12
Exercise 6b
Day Sample Mean
Sat 20.3
Sun 19.3
Mon 17.0
Tue 19.0
Wed 21.0
Thu 18.7
Sum 115.3
15.45)1.023(3.67-19.21 LCL
96.22 )1.023(3.6719.21 UCL
023.1A
21.196/3.115X
2
For Friday the sample mean is 16.7, so the process is in control.
Chapter 3: Quality Management 13
Exercise 6b concluded
22.96
19.21
15.45
Sat Sun Mon Tue Wed Thu Fri
UCL
LCL
**
**
*
**
14
Exercise 7
606.)1.1(6
2832
pC
Dough Boy’s pizza crust production system is not capable of consistently meeting its customer requirements given the Cp index of less than 1. Options available to Dough Boy include improving its production system to lower the natural variation in the system. In this case, Dough Boy needs to reduce the standard deviation of pizza crusts from 1.1 to .66 or lower in order to obtain a Cp index of 1 or more. Alternatively, Dough Boy could try to convince its customers to increase the range of acceptable pizza crust diameters.
Chapter 3: Quality Management 15
Exercise 8
0.83 0.83) ,33.1min(
83.)2(3
350355
33.1)2(3
355363
08.1)2(6
350363
pk
pl
pu
p
C
C
C
C The Cp index indicates that given the natural variation in the filling operation, it is capable of meeting the design specifications. However, when the alignment of the process mean and the design specification is considered, it is found that the filling operation is not capable of consistently meeting design requirements.
Chapter 3: Quality Management 16
Exercise 9a
Total number of cases = 27,400
Total incorrect = 235
0 3(.00922)-.00857 LCL
.03623 3(.00922).00857UCL
3
00922.100
)00857.1(00857.
00857.400,27
235
p
p
p
p
Chapter 3: Quality Management 17
Exercise 9a concluded
.03623
.00857
0.0
UCL
LCL
Chapter 3: Quality Management 18
Exercise 9b: Day 7
.0044 3(.0014)-.0086LCL
.01283(.0014).0086UCL
00136.4600
)00857.1(00857.
p
On day 7, p = .0115, therefore process is in control.
Chapter 3: Quality Management 19
Exercise 9b: Day 8
.0050 3(.0012)-.0086LCL
.01223(.0012).0086UCL
0012.6100
)00857.1(00857.
p
On day 8, p = .0093, therefore process is in control.
Chapter 3: Quality Management 20
Exercise 9b: Day 9
.0041 3(.0015)-.0086LCL
.01313(.0015).0086UCL
0015.3900
)00857.1(00857.
p
On day 9, p = .0123, therefore process is in control.
Chapter 3: Quality Management 21
Exercise 10
X p c
Mon 25 .000025 25
Tue 36 .000036 36
Wed 17 .000017 17
Sum 78 .000078 78
Avg. 26 .000026 26
Chapter 3: Quality Management 22
Exercise 10: Sample Means Chart
A2 = 1.023; Range 36 - 17 = 19
UCL = 26 + 1.023(19) = 45.44
LCL = 26 - 1.023(19) = 6.56
Thursday’s 47 defectives is outside control limits.
Chapter 3: Quality Management 23
Exercise 10: p chart
.0000107 )3(.0000051-.000026 LCL
.0000413)3(.0000051.000026UCL
0000051.000,000,1
)000026.1(000026.
p
On Thursday, p = .000047, therefore not in control.
Chapter 3: Quality Management 24
Exercise 10: c chart
10.7 3(5.1) - 26 LCL
41.3 3(5.1) 26UCL
1.526
26
c
c
On Thursday, 47 are defective. Thus, out of control.
Chapter 3: Quality Management 25
Exercise 10 concluded
• The c chart is most appropriate
• The p chart is acceptable
• The sample means chart is not appropriate