# ISS (Statistical Services) Statistics Paper IV: Questions 16 - 19 of 92

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## Question 16

### Describe in Detail

Essay▾

a) What are control charts for Attributes?

b) A quality control inspector at the Pepsi soft drink company has taken twenty-five samples with four observations each of the volume of bottles filled. If the average range for the twenty-five samples is . 29 ounces and the average mean of the observations is 15.95 ounces, obtain 3- σ control limits for ?

### Explanation

a) To measure the quality characteristics, Control charts for attributes are used, that are counted rather than measured. P-charts and C-charts are common types of control charts used to measure the attributes.

P-charts measure the proportion of items in a sample that are defective. For example, proportion of broken eggs and the proportion of cars p&#8230;

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## Question 17

### Describe in Detail

Essay▾

Following data gives the diameter of the rings manufactured by a company. Obtain the control limits for R Chart?

 Sample No. Observations 1 5.02 5.01 4.94 4.99 4.96 2 5.01 5.03 5.07 4.95 4.96 3 4.99 5.00 4.93 4.92 4.99 4 5.03 4.91 5.01 4.98 4.89 5 4.95 4.92 5.03 5.05 5.01 6 4.97 5.06 5.06 4.96 5.03 7 5.05 5.01 5.10 4.96 4.99 8 5.09 5.10 5.00 4.99 5.08 9 5.14 5.10 4.99 5.08 5.09 10 5.01 4.98 5.08 5.07 4.99

### Explanation

From the tables, for n = 10, we have ,

Control limits for R chart :

= (0.223) (0.115) = 0.0256

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## Question 18

Appeared in Year: 2015

### Describe in Detail

Essay▾

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 constraints of eq (1) , we get

Summing n-1 constraints of eq (2) , we get

Subtracting eq (4) from eq (3) , we get

Which is the last con&#8230;

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## Question 19

### Describe in Detail

Essay▾

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&#8230;

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