# ISS (Statistical Services) Statistics Paper IV: Questions 34 - 36 of 92

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## Question 34

### Describe in Detail

Essay▾

A machine is manufacturing mica discs. Samples of size 5 are drawn every hour and their thickness in units are recorded as follows. Based on chart, Check whether the production is under control?

 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

Since all the points fall within the control limits, the process is under control.

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## Question 35

### Describe in Detail

Essay▾

Construct control limits for chart for the following data based on electric fuses, samples of 5 being taken every hour. Using, R-charts test whether the production is under control?

 Sample No. Observations 1 42 65 75 78 87 2 42 45 68 72 90 3 19 24 80 81 81 4 36 54 69 77 84 5 42 51 57 59 78 6 51 74 75 78 132 7 60 60 72 95 138 8 18 20 27 42 60 9 15 30 39 62 84 10 69 109 113 118 153 11 64 90 93 109 112 12 61 78 94 109 136

### Explanation

From the above data we get

From the tables, for n = 5, ,

Control limits for R :

= 0

Since all the sample points fall within the control limits, R chart shows the process is in control.

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## Question 36

### Describe in Detail

Essay▾

Following is the data of 25 samples with 4 observations on the basis of volume of the bottles filled. Using a control limits for chart, Test whether the production is under control?

 Sample No. Observations Sample No. Observations 1 15.85 16.02 15.83 15.93 13 15.85 15.76 15.74 15.98 2 16.12 16.00 15.85 16.01 14 15.73 15.84 15.96 16.10 3 16.00 15.91 15.94 15.83 15 16.20 16.01 16.10 15.89 4 16.20 15.85 15.74 15.93 16 16.12 16.08 15.83 15.94 5 15.74 15.86 16.21 16.10 17 16.01 15.93 15.81 15.68 6 15.94 16.01 16.14 16.03 18 15.78 16.04 16.11 16.12 7 15.75 16.21 16.01 15.86 19 15.84 15.92 16.05 16.12 8 15.82 15.94 16.02 15.94 20 15.92 16.09 16.12 15.93 9 16.04 15.98 15.83 15.98 21 16.11 16.02 16.00 15.88 10 15.64 15.86 15.94 15.89 22 15.98 15.82 15.89 15.89 11 16.11 16.00 16.01 15.82 23 16.05 15.73 15.73 15.93 12 15.72 15.85 16.12 16.15 24 16.01 16.01 15.89 15.86 25 16.08 15.78 15.92 15.98

### Explanation

From the above data we get

From the tables, for n = 4, we have

Control limits for :

And

Since all the sample points falls within the control limits process is under control.

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