# 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

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
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