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 (R¯) for the twenty-five samples is. 29 ounces and the average mean (X̿) of the observations is 15.95 ounces, obtain 3- σ control limits for X¯chart ?

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… (171 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… (114 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 m+n1 , 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 m+n1 equation in mn variables and hence at most m+n1 basic variable are there. We note… (263 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 X¯ chart. If we are given that μ=15.95 σ = 0.14 and n = 4 construct control limits for X¯chart ?

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… (256 more words) …

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