ISS (Statistical Services) 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 Equation for the twenty-five samples is. 29 ounces and the average mean Equation Equation of the observations is 15.95 ounces, obtain 3- σ control limits for Equation ?

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?

Given values with observations

Sample is given with observations

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

Given values with observations Calculate range

Sample is given with observations

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

» Operations Research and Reliability » Finding Solutions in 22, 2xm and Mxn Games

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Prove that the number of basic variables is a balanced transportation problem is at most Equation , 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 equation in mn variables and hence at most Equation basic variable are there. We note

Equation

Equation

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 Equation chart. If we are given that μ=15.95 σ = 0.14 and n = 4 construct control limits for Equation ?

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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