# ISS Statistics Paper IV: Questions 16 - 19 of 79

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## Question number: 16

» Statistical Quality Control » Control Charts » Variable

Essay Question▾

### Describe in Detail

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 meanof 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… (84 more words) …

## Question number: 17

» Statistical Quality Control » Control Charts » Variable

Essay Question▾

### Describe in Detail

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

 Sample No. Observations Range 1 5.02 5.01 4.94 4.99 4.96 0.08 2 5.01 5.03 5.07 4.95 4.96 0.12 3 4.99 5.00 4.93 4.92 4.99 0.08 4 5.03 4.91 5.01 4.98 4.89 0.14 5 4.95 4.92 5.03 5.05 5.01 0.13… (62 more words) …

## Question number: 18

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 constraints of eq… (57 more words) …

## Question number: 19

» Statistical Quality Control » Control Charts » Variable

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… (128 more words) …

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