# Statistical Quality Control (ISS (Statistical Services) Statistics Paper IV): Questions 27 - 29 of 34

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## Question number: 27

» Statistical Quality Control » Control Charts » Variable

Essay Question▾

### Describe in Detail

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

 Sample No. Observations Sample Range 1 8 9 15 4 11 11 2 7 10 7 6 8 4 3 11 12 10 9 10 3 4 12 8 6 9 12 6 5 11 10 6 14 11 8 6 7 7 10 4 11 7 7 10 7 4 10 10 6 8 8 11 11 7 7 4 9 8 11 8 14 12 6 10 12 9 12 17 11 8 11 7 7 9 17 13 10 12 9 9 4 4 11 7 13 10 12 12 12 12 2 14 8 11 9 6 8 5 15 10 13 9 4 9 9 16 9 11 8 5 11 6 Total 102

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## Question number: 28

» Statistical Quality Control » Control Charts » Variable

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### Describe in Detail

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

 Sample No. Observations Sample Range 1 42 65 75 78 87 87 45 2 42 45 68 72 90 90 48 3 19 24 80 81 81 81 62 4 36 54 69 77 84 84 48 5 42 51 57 59 78 78 36 6 51 74 75 78 132 132 81 7 60 60 72 95 138 138 78 8 18 20 27 42 60 60 42 9 15 30 39 62 84 84 69 10 69 109 113 118 153 153 84 11 64 90 93 109 112 112 48 12 61 78 94 109 136 136 75 716

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## Question number: 29

» Statistical Quality Control » Control Charts » Variable

Essay Question▾

### Describe in Detail

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

 Sample No. Observations Total Sample Mean Range 1 15.85 16.02 15.83 15.93 63.63 15.91 0.19 2 16.12 16.00 15.85 16.01 63.98 16.00 0.27 3 16.00 15.91 15.94 15.83 63.68 15.92 0.17 4 16.20 15.85 15.74 15.93 63.72 15.93 0.46 5 15.74 15.86 16.21 16.10 63.91 15.98 0.47 6 15.94 16.01 16.14 16.03 64.12 16.03 0.20 7 15.75 16.21 16.01 15.86 63.83 15.96 0.46 8 15.82 15.94 16.02 15.94 63.72 15.93 0.20 9 16.04 15.98 15.83 15.98 63.83 15.96 0.21 10 15.64 15.86 15.94 15.89 63.33 15.83 0.30 11 16.11 16.00 16.01 15.82 63.94 15.99 0.29 12 15.72 15.85 16.12 16.15 63.84 15.96 0.43 13 15.85 15.76 15.74 15.98 63.33 15.83 0.24 14 15.73 15.84 15.96 16.10 63.63 15.91 0.37 15 16.20 16.01 16.10 15.89 64.20 16.05 0.31 16 16.12 16.08 15.83 15.94 63.97 15.99 0.29 17 16.01 15.93 15.81 15.68 63.43 15.86 0.33 18 15.78 16.04 16.11 16.12 64.05 16.01 0.34 19 15.84 15.92 16.05 16.12 63.93 15.98 0.28 20 15.92 16.09 16.12 15.93 64.06 16.02 0.20 21 16.11 16.02 16.00 15.88 64.01 16.00 0.23 22 15.98 15.82 15.89 15.89 63.58 15.90 0.16 23 16.05 15.73 15.73 15.93 63.44 15.86 0.32 24 16.01 16.01 15.89 15.86 63.77 15.94 0.15 25 16.08 15.78 15.92 15.98 63.76 15.94 0.30 398.67 7.17

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