ISS (Statistical Services) Statistics Paper IV: Questions 28 - 30 of 79
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Question number: 28
» Statistical Quality Control » Control Charts » Attributes
Describe in Detail
The following are the figures of defectives in 22 lots each containing 2, 000 bulbs. Ind control limit for p-Chart.
|
425
|
430
|
216
|
341
|
225
|
322
|
280
|
306
|
337
|
305
|
356
|
|
402
|
216
|
264
|
126
|
409
|
193
|
326
|
280
|
389
|
451
|
420 |
Explanation
We have n = 2000
|
S. No.
|
d
|
|
|
1
|
425
|
0.2125
|
|
2
|
430
|
0.215
|
|
3
|
216
|
0.108
|
|
4
|
341
|
0.1705
|
|
5
|
225
|
0.1125
|
|
6
|
322
|
0.161
|
|
7… (105 more words) … |
Question number: 29
» Statistical Quality Control » Control Charts » Attributes
Describe in Detail
Each day a sample of 1500 items from a production process was examined. The number of defectives found in each sample was as follows. With a suitable control chart, check out for control 4, 6, 6, 2, 15, 4, 4
Explanation
We have n = 30
|
S. No.
|
d
|
|
|
1
|
4
|
0.00267
|
|
2
|
6
|
0.00400
|
|
3
|
6
|
0.00400
|
|
4
|
2
|
0.00133
|
|
5
|
15
|
0.01000
|
|
6
|
4
|
0.00267… (61 more words) … |
Question number: 30
» Statistical Quality Control » Control Charts » Variable
Describe in Detail
a) The number of customer complaints are recorded at a television manufacturing company. Complaints have been recorded over the past 20 weeks. Construct 3-σ control limits for the c-chart.
|
Week
|
No. of complaints
|
Week
|
No. of complaints
|
|
1
|
0
|
11
|
4
|
|
2
|
3
|
12
|
3
|
|
3
|
4
|
13
|
1
|
|
4
|
1
|
14
|
1
|
|
5
|
0
|
15
|
1
|
|
6
|
0
|
16
|
0
|
|
7
|
3
|
17
|
2
|
|
8
|
1
|
18
|
1
|
|
9
|
1
|
19
|
2
|
|
10
|
0
|
20
|
2
|
b) A machine is manufacturing mica discs. samples of size 5 are drawn every hour and their thickness in units are recorded as follows. From this data construct 3-σ control limits for chart.
|
Sample No.
|
Observstions
| ||||
|
1
|
8
|
9
|
15
|
4
|
11
|
|
2
|
7
|
10
|
7
|
6
|
8
|
|
3
|
11
|
12
|
10
|
9
|
10
|
|
4
|
12
|
8
|
6
|
9
|
12
|
|
5
|
11
|
10
|
6
|
14
|
11
|
|
6
|
7
|
7
|
10
|
4
|
11
|
|
7
|
10
|
7
|
4
|
10
|
10
|
|
8
|
8
|
11
|
11
|
7
|
7
|
|
9
|
8
|
11
|
8
|
14
|
12
|
|
10
|
12
|
9
|
12
|
17
|
11
|
|
11
|
7
|
7
|
9
|
17
|
13
|
|
12
|
9
|
9
|
4
|
4
|
11
|
|
13
|
10
|
12
|
12
|
12
|
12
|
|
14
|
8
|
11
|
9
|
6
|
8
|
|
15
|
10
|
13
|
9
|
4
|
9
|
|
16
|
9
|
11
|
8
|
5
|
11 |
Explanation
a) Average number of defects per sample is
=1.5+ =1.5 + 3 (1.22) =5.174
= →0
Since number of defects cannot be negative, can be considered as zero. (rounded up to zero)
b) Second question: