Six
samples of n = 20 observations have been obtained and the
sample means and ranges computed:
Sample
Mean
Range
Sample
Mean
Range
1
3.06
.42
4
3.13
.46
2
3.15
.38
5
3.06
.46
3
3.11
.41
6
3.09
.45
Factors for three-sigma control limits for and R charts
FACTORS FOR
R CHARTS
Number
of Observations in Subgroup,n
Factor
for
Chart,A2
Lower
Control Limit,D3
Upper
Control Limit,D4
2
1.88
0
3.27
3
1.02
0
2.57
4
0.73
0
2.28
5
0.58
0
2.11
6
0.48
0
2.00
7
0.42
0.08
1.92
8
0.37
0.14
1.86
9
0.34
0.18
1.82
10
0.31
0.22
1.78
11
0.29
0.26
1.74
12
0.27
0.28
1.72
13
0.25
0.31
1.69
14
0.24
0.33
1.67
15
0.22
0.35
1.65
16
0.21
0.36
1.64
17
0.20
0.38
1.62
18
0.19
0.39
1.61
19
0.19
0.40
1.60
20
0.18
0.41
1.59
a.
Using the factors in the above
table, determine upper and lower limits for mean and range charts.(Round your intermediate calculations and final answers to
4 decimal places.)
Upper limit for mean
Lower limit for mean
Upper limit for range
Lower limit for range
b.
Is the process in control?
Yes
No
Problem 10-4
Computer upgrades have a nominal
time of 80 minutes. Samples of five observations each have been taken, and
the results are as listed.
SAMPLE
1
2
3
4
5
6
79.2
80.5
79.6
78.9
80.5
79.7
78.8
78.7
79.6
79.4
79.6
80.6
80.0
81.0
80.4
79.7
80.4
80.5
78.4
80.4
80.3
79.4
80.8
80.0
80.2
80.1
80.8
80.6
78.8
81.1
Factors for three-sigma control
limits for and R charts
FACTORS FOR R CHARTS
Number
of Observations in Subgroup,n
Factor
for
Chart,A2
Lower
Control Limit,D3
Upper
Control Limit,D4
2
1.88
0
3.27
3
1.02
0
2.57
4
0.73
0
2.28
5
0.58
0
2.11
6
0.48
0
2.00
7
0.42
0.08
1.92
8
0.37
0.14
1.86
9
0.34
0.18
1.82
10
0.31
0.22
1.78
11
0.29
0.26
1.74
12
0.27
0.28
1.72
13
0.25
0.31
1.69
14
0.24
0.33
1.67
15
0.22
0.35
1.65
16
0.21
0.36
1.64
17
0.20
0.38
1.62
18
0.19
0.39
1.61
19
0.19
0.40
1.60
20
0.18
0.41
1.59
a.
Using factors from
above table, determine upper and lower control limits for mean and range
charts.(Round your intermediate calculations and
final answers to 2 decimal places. Leave no cells blank – be certain to
enter “0” wherever required.)
Mean
Chart
Range
Chart
UCL
LCL
b.
Decide if the process is in
control.
Yes
No
Problem 10-6
A
medical facility does MRIs for sports injuries. Occasionally a test yields
inconclusive results and must be repeated. Using the following sample data
and n = 192.
SAMPLE
1
2
3
4
5
6
7
8
9
10
11
12
13
Number of
retests
1
1
2
0
2
1
1
0
2
9
4
2
1
a.
Determine
the upper and lower control limits for the fraction of retests using
two-sigma limits. (Do not round intermediate calculations. Round your
final answers to 4 decimal places. Leave no cells blank – be certain to
enter “0” wherever required.)
UCL
LCL
b.
Is the process in
control?
Yes
No
Problem 10-7
The postmaster of a small western
town receives a certain number of complaints each day about mail delivery.
DAY
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Number of complaints
4
12
15
8
9
6
5
13
14
7
6
4
2
10
a.
Determine two-sigma control limits
using the above data. (Round your
intermediate calculations to 4 decimal places and final answers to
3 decimal places. Leave no cells blank – be certain to enter “0”
wherever required.)
UCL
LCL
b.
Is the process in control?
No
Yes
Problem 10-8
Given the following data for the
number of defects per spool of cable.
OBSERVATION
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Number of defects
1
3
1
0
1
3
2
0
2
4
3
1
2
0
a.
Determine three-sigma control
limits using the above data. (Do not round
intermediate calculations. Round your final answers to 2 decimal
places. Leave no cells blank – be certain to enter “0” wherever
required.)
UCL
LCL
b.
Is the process in control?
Yes
No