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Five data entry operators work at the data processing department of the Birmingh

ID: 3170513 • Letter: F

Question

Five data entry operators work at the data processing department of the Birmingham Bank. Each day for 30 days, the number of defective records in a sample of 300 records typed by these operators has been noted, as follows:

  

Sample No.

No. Defectives

Sample No.

No. Defectives

Sample No.

No. Defectives

1

88

11

77

21

1717

2

44

12

55

22

1313

3

1919

13

1616

23

66

4

1010

14

33

24

66

5

1212

15

1212

25

1313

6

99

16

88

26

1111

7

1111

17

1313

27

1515

8

1010

18

44

28

77

9

66

19

1818

29

1313

10

1414

20

1717

30

44

a) Establish 3 upper and lower control limits.

UCLp = (enter your response as a number between 0 and 1, rounded to three decimal places).

LCPp =(enter your response as a number between 0 and 1, rounded to three decimal places).

b) Why can the lower limit not be a negative number? (I actually know this one but I wanna get all the points down)

c) The industry standards for the upper and lower control limits are 0.10 and 0.01, respectively. What does this imply about Birmingham Bank's own standards?

Sample No.

No. Defectives

Sample No.

No. Defectives

Sample No.

No. Defectives

1

88

11

77

21

1717

2

44

12

55

22

1313

3

1919

13

1616

23

66

4

1010

14

33

24

66

5

1212

15

1212

25

1313

6

99

16

88

26

1111

7

1111

17

1313

27

1515

8

1010

18

44

28

77

9

66

19

1818

29

1313

10

1414

20

1717

30

44

Explanation / Answer

This can be considered a basic problem of Statistical Quality Control and control charts.

a) 3sigma upper limits can be obtained easily by simple calculation in excel sheet as follows:

upper limit is : mean + 3 x S.D. = 9.67 + 3 x 4.54 =23.29 3sigma

lower limit is : 9.67 - 3 X 4.54 = 0 (Since it cant be less than 0 )

b) Lower limit cant be a negative number because any data number like defects cant be negative. I guess this is the only thing that you knew.

c) Upper control limits is 0.10

Thus the upper limit = 9.67 + 1.645 x 4.54 =17.13

[ p value for 90% confidence level = 1.65]

Similarly we compute the lower limit also.