Quality Control Classroom Problems
1. Checkout time at a supermarket is monitored using a mean and a range chart. Six
samples of n=20 observations have been obtained and the sample means and ranges
computed:
Sample
1
2
3
4
5
6
Mean
3.06
3.15
3.11
3.13
3.06
3.09
Range
.42
.50
.41
.46
.46
.45
a. Using the factors Table in 10.3, determine the upper and lower limits for mean and
range charts.
b. Is the process in control?
2. Processing new accounts at a bank is intended to average 10 minutes each. Five
samples of four observations each have been taken. Use the sample data in conjunction
with Table in 10.3 to construct the upper and lower control limits for both a mean chart
and a range chart. Do the results suggest the process is in control?
Sample 1
Sample 2
Sample 3
10.2
10.3
9.7
9.9
9.8
9.9
9.8
9.9
9.9
10.1
10.4
10.1
Total = 40.0
Total = 40.4
Total =39.6
a. Determine the mean and range of each sample.
b. Compute the average mean and average range.
c. Obtain factors A(2), D(4), and D(3) for n=4
d. Compute the upper and lower limits.
Sample 4
9.9
10.3
10.1
10.5
Total =40.8
Sample 5
9.8
10.2
10.3
9.7
Total =40.0
3. Hospital Admin inventories the quality of meals. Surveys 10 days with 1000 responses
per day.
Day
1
2
3
4
5
6
7
8
9
10
Total
Unsatisfactory
74
42
64
80
40
50
65
70
40
75
600
Sample Size
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
10,000
Percentage
.074
.042
.064
.080
.040
.050
.065
.070
.040
.075
a. Construct a P chart with a 95.4% confidence level. Z = 2, Sigma = 2
b. Is the process in control?
4. The postmaster of a small western town receives a certain number of complaints each
day about mail delivery. Determine three-sigma control limits using the following data.
Is the process in control?
#
1
4
2
10
3
14
4
8
# = Number of complaints
Z=3
5
9
6
6
7
5
8
12
9
13
10
7
11
6
12
4
13
2
14
10
Table 10.3
Number of
Observations per
Group (n)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Factors for X chart
A(2)
1.88
1.02
.73
.58
.48
.42
.37
.34
.31
.29
.27
.25
.24
.22
.21
.20
.19
.19
.18
Factors for R chart
Lower control limit
D(3)
0
0
0
0
0
.08
.14
.18
.22
.26
.28
.31
.33
.35
.36
.38
.39
.40
.41
Factors for R chart
Upper control limit
D(4)
3.27
2.57
2.28
2.11
2.00
1.92
1.86
1.82
1.78
1.74
1.72
1.69
1.87
1.65
1.64
1.62
1.61
1.60
1.59