Answer to 1st Question:
The following table shows the calculations -
Month |
Number of Defectives in each sample |
Proportion defective(pi) |
1 |
8 |
0.1333 |
2 |
7 |
0.1167 |
3 |
2 |
0.0333 |
4 |
8 |
0.1333 |
5 |
4 |
0.0667 |
6 |
5 |
0.0833 |
7 |
12 |
0.2 |
8 |
7 |
0.1167 |
9 |
9 |
0.15 |
10 |
6 |
0.1 |
11 |
6 |
0.1 |
12 |
14 |
0.2333 |
Total |
1.4666 |
Mean proportion defective, = 1.4666 / 12 = 0.12(approximately)
Number of observations, n = 12
The formula for control limits -
U.C.L. = + A ( (1 - ) )0.5 (where, A = 3 / n0.5)
L.C.L. = - A ( (1 - ) )0.5 (where, A = 3 / n0.5)
Substituting the values,
U.C.L. = 0.41
L.C.L. = -0.1614
Since, L.C.L. is negative it would be taken as 0
Therefore,
Mean Proportion Defective |
0.12 |
U.C.L. |
0.41 |
L.C.L. |
0 |
Answer to 2nd Question:
Since all the observations lie inside the control limits, the
number of complaints are not out-of-control
Hence, NO is the correct option
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