Operation and Supply Chain Management stuck

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