# ISS (Statistical Services) Statistics Paper IV: Questions 18 - 21 of 92

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## Question number: 18

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Prove that the number of basic variables is a balanced transportation problem is at most , where m is the number of origins and n is the number of destinations.

### Explanation

First note that there are in all m + n constraints. We shall show that one of these is redundant so that there are in effect equation in mn variables and hence at most basic variable are there. We note

Summing the m cons

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## Question number: 19

» Statistical Quality Control » Control Charts » Variable

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Essay Question▾

### Describe in Detail

What are control charts for variables? Find 3- σ control limits on the chart. If we are given that μ=15.95 σ=0.14 and n = 4 construct control limits for ?

### Explanation

Control chart for variables are used to monitor characteristics that can be measured, e. g. length, weight, diameter, time etc. When a record is made of an actual measured quality characteristic like dimension expressed as hundredths of a millimeter, the quality is expressed by variables. For quality control of such data, two types of control chart

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## Question number: 20

» Statistical Quality Control » Control Charts » Attributes

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Essay Question▾

### Describe in Detail

The following are figures of defective bulbs in 10 lots each containing 30 bulbs. Construct 3-σ control limits for the p-chart.

 Sample No. of defective (d) 1 1 2 3 3 3 4 1 5 0 6 5 7 1 8 1 9 1 10 1

### Explanation

We have n = 30

 Sample No. of defective (d) 1 1 0.033 2 3 0.100 3 3 0.100 4 1 0.033 5 0 0.000 6 5 0.167 7 1 0.033 8 1 0.033 9 1 0.033 10 1 0.033 Total 0.567

Control limits for charts

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## Question number: 21

» Statistical Quality Control » Control Charts » Variable

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Essay Question▾

### Describe in Detail

Obtain the control limits for for the following data of 25 samples with 4 observations on the basis of volume of the bottles filled.

 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

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