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