Solutions to Chapter 3 Exercises

1
Solutions to Chapter 3 Exercises

2
Exercise 1
3
Exercise 2
4
Exercise 2 continued

• The upward trend in cancellations and
  non-renewals is a definite cause for concern.

5
Exercise 3
6
Exercise 3 concluded
1.2826 1.02 .7574
UCL






LCL
Jun Jul Aug Sep Oct Nov
7
Exercise 4
Xi 3,500
4,100 3,750
4,300 4,000 3,650
Total 23,300
8
Exercise 5
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.
10
Exercise 6a
Day Range Sat 3 Sun 4 Mon
2 Tue 5 Wed 3 Thu
5 Sum 22
For Friday the range is 7, so the range on Friday
is in control.
11
Exercise 6a concluded
9.45 3.67 0
UCL







LCL
Sat Sun Mon Tue Wed Thu Fri
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
For Friday the sample mean is 16.7, so the
process is in control.
13
Exercise 6b concluded
22.96 19.21 15.45
UCL







LCL
Sat Sun Mon Tue Wed Thu Fri
14
Exercise 7
Dough Boys 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.
15
Exercise 8
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.
16
Exercise 9a
Total number of cases 27,400 Total incorrect
235
17
Exercise 9a concluded
.03623 .00857 0.0
UCL
LCL
18
Exercise 9b Day 7
On day 7, p .0115, therefore process is in
control.
19
Exercise 9b Day 8
On day 8, p .0093, therefore process is in
control.
20
Exercise 9b Day 9
On day 9, p .0123, therefore process is in
control.
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
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 Thursdays 47 defectives is outside control
limits.
23
Exercise 10 p chart
On Thursday, p .000047, therefore not in
control.
24
Exercise 10 c chart
On Thursday, 47 are defective. Thus, out of
control.
25
Exercise 10 concluded

• The c chart is most appropriate
• The p chart is acceptable
• The sample means chart is not appropriate