Develop three-sigma control limits for bottling operation


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Q: A quality control inspector at Cocoa Fizz is using the data from above to develop control limits. If the average range for the twenty-five samples is .29 ounces (computed as 7.17/25) and the average mean of the observations is 15.95 ounces, develop three-sigma control limits for the bottling operation without knowing the standard deviation of the population.


Observations




Sample

(bottle volume in ounces)

Average

Range

Number

1

2

3

4


R

1

15.85

16.02

15.83

15.93

15.91

0.19

2

16.12

16.00

15.85

16.01

15.99

0.27

3

16.00

15.91

15.94

15.83

15.92

0.17

4

16.20

15.85

15.74

15.93

15.93

0.46

5

15.74

15.86

16.21

16.10

15.98

0.47

6

15.94

16.01

16.14

16.03

16.03

0.20

7

15.75

16.21

16.01

15.86

15.96

0.46

8

15.82

15.94

16.02

15.94

15.93

0.20

9

16.04

15.98

15.83

15.98

15.96

0.21

10

15.64

15.86

15.94

15.89

15.83

0.30

11

16.11

16.00

16.01

15.82

15.99

0.29

12

15.72

15.85

16.12

16.15

15.96

0.43

13

15.85

15.76

15.74

15.98

15.83

0.24

14

15.73

15.84

15.96

16.10

15.91

0.37

15

16.20

16.01

16.10

15.89

16.05

0.31

16

16.12

16.08

15.83

15.94

15.99

0.29

17

16.01

15.93

15.81

15.68

15.86

0.33

18

15.78

16.04

16.11

16.12

16.01

0.34

19

15.84

15.92

16.05

16.12

15.98

0.28

20

15.92

16.09

16.12

15.93

16.02

0.20

21

16.11

16.02

16.00

15.88

16.00

0.23

22

15.98

15.82

15.89

15.89

15.90

0.16

23

16.05

15.73

15.73

15.93

15.86

0.32

24

16.01

16.01

15.89

15.86

15.94

0.15

25

16.08

15.78

15.92

15.98

15.94

0.30

Total





398.75

7.17

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Operation Management: Develop three-sigma control limits for bottling operation
Reference No:- TGS02044395

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