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

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Question 9

Describe in Detail

Essay▾

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 10

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Essay▾

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 18 326 0.163 19 280 0.14 20 389 0.1945 21 451 0.2255 22 420 0.21 Total 3.5095

Control limits for :

3-σcontrol limits for the p ch…

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Question 11

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Essay▾

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

The control chart shows that a observation corresponding to the 11th sample falls outside the control limits indicating that the process is not in control.

Control limits for R chart :

= 0

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