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 | 280 | 0.14 |
| 8 | 306 | 0.153 |
| 9 | 337 | 0.1685 |
| 10 | 305 | 0.1525 |
… (79 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 |
| 7 | 4 | 0.00267 |
| Total | 41 | 0.02733 |
Cont
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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:
| Sample No. | Observations | Total | Sample Mean | Sample Range | ||||
| 1 | 8 | 9 | 15 | 4 | 11 | 47 | 9.4 | 11 |
| 2 | 7 | 10 | 7 | 6 | 8 | 38 | 7.6 | 4 |
| 3 | 11 | 12 | 10 | 9 | 10 | 52 | 10.4 | 3 |
| 4 | 12 | 8 | 6 | 9 | 12 | 47 | 9.4 | 6 |
| 5 | 11 | 10 | 6 | 14 | 11 | 52 | 10.4 | 8 |
| 6 | 7 | 7 | 10 | 4 | 11 | 39 | 7.8 | 7 |
| 7 | 10 | 7 | 4 | 10 | 10 | 41 | 8.2 | 6 |
| 8 | 8 | 11 | 11 | 7 | 7 | 44 | 8.8 | 4 |
| 9 | 8 | 11 | 8 | 14 | 12 | 53 | 10.6 | 6 |
| 10 | 12 | 9 | 12 | 17 | 11 | 61 | 12.2 | 8 |
| 11 | 7 | 7 | 9 | 17 | 13 | 53 | 10.6 | 10 |
| 12 | 9 | 9 | 4 | 4 | 11 | 37 | 7.4 | 7 |
| 13 | 10 | 12 | 12 | 12 | 12 | 58 | 11.6 | 2 |
| 14 | 8 | 11 | 9 | 6 | 8 | 42 | 8.4 | 5 |
| 15 | 10 | 13 | 9 | 4 | 9 | 45 | 9 | 9 |
| 16 | 9 | 11 | 8 | 5 | 11 | 44 | 8.8 | 6 |
| Total | 150.6 | 102 | ||||||
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