ISS (Statistical Services) Statistics Paper IV: Questions 16  19 of 79
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Question number: 16
» Statistical Quality Control » Control Charts » Variable
Describe in Detail
a) What are control charts for Attributes?
b) A quality control inspector at the Pepsi soft drink company has taken twentyfive samples with four observations each of the volume of bottles filled. If the average range for the twentyfive 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. Pcharts and Ccharts are common types of control charts used to measure the attributes.
Pcharts measure the proportion of items in a sample that are defective. For example, proportion of broken eggs
Question number: 17
» Statistical Quality Control » Control Charts » Variable
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 
Question number: 18
» Operations Research and Reliability » Finding Solutions in 22, 2xm and Mxn Games
Appeared in Year: 2015
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
Question number: 19
» Statistical Quality Control » Control Charts » Variable
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