# ISS (Statistical Services) Statistics Paper IV: Questions 9 - 11 of 92

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## Question number: 9

» Statistical Quality Control » Control Charts » Variable

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### Describe in Detail

A machine is manufacturing mica discs. Samples of size 5 are drawn every hour and their thickness in units is recorded as follows. From this data construct 3-σ control limits for and R charts.

 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

Control limits for R chart:

For n = 5, from the tables we the value of and

=0

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## Question number: 10

» Statistical Quality Control » Control Charts » Attributes

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The following are the figures of defectives in 22 lots each containing 2,000 bulbs. Obtain the 3-σ control limits for the 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 11 356 0.178 12 402 0.201 13 216 0.108 14 264 0.132 15 126 0.063 16 409 0.2045 17 193 0.0965

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## Question number: 11

» Statistical Quality Control » Control Charts » Variable

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### Describe in Detail

A electric Company uses a process to paint cars with a coat of enamel. During each shift, a sample of five cars is selected and the thickness of the paint in mm is determined. On the basis of and R charts, Check whether the production is under control?

 Sample No. Observations 1 2.6 2.3 2.6 2.7 2.7 2 2.6 2.6 2.4 2.8 2.3 3 2.4 2.3 2.4 2.5 2.3 4 2.7 2.4 2.3 2.6 2.8 5 2.6 2.6 2.5 2.8 2.1 6 2.2 2.2 2.7 2.3 2.6 7 2.0 2.6 2.4 2.2 2.3 8 2.5 2.6 2.6 2.7 2.8 9 2.4 2.4 2.2 2.8 2.3 10 2.6 2.3 2.0 2.5 2.4 11 3.1 3.0 3.5 2.8 3.0 12 2.4 2.8 2.2 2.9 2.5 13 2.1 3.2 2.5 2.6 2.8 14 2.2 2.8 2.1 2.2 2.4 15 2.4 3.0 2.5 2.5 2.0 16 3.1 2.6 2.6 2.8 2.1 17 2.9 2.4 2.9 1.3 1.8 18 1.9 1.6 2.6 3.3 3.3 19 2.3 2.6 2.7 2.8 3.2 20 2.0 2.8 2.3 1.8 2.9

### Explanation

From the tables, for n = 5, we have , ,

Control limits for :

And

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