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.
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