ISS (Statistical Services) Statistics Paper IV: Questions 18 - 21 of 92

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Question number: 18

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

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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 cons

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Question number: 19

» Statistical Quality Control » Control Charts » Variable

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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 data, two types of control chart

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Question number: 20

» Statistical Quality Control » Control Charts » Attributes

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Essay Question▾

Describe in Detail

The following are figures of defective bulbs in 10 lots each containing 30 bulbs. Construct 3-σ control limits for the p-chart.

Construct 3 sigma control limit for p-chart

What is the 3 sigma control limit for p-chart

Sample

No. of defective (d)

1

1

2

3

3

3

4

1

5

0

6

5

7

1

8

1

9

1

10

1

Explanation

We have n = 30

Construct 3 sigma control limit for p-chart Finding Defectives

What is the 3 sigma control limit for p-chart

Sample

No. of defective (d)

1

1

0.033

2

3

0.100

3

3

0.100

4

1

0.033

5

0

0.000

6

5

0.167

7

1

0.033

8

1

0.033

9

1

0.033

10

1

0.033

Total

0.567

Control limits for charts

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Question number: 21

» Statistical Quality Control » Control Charts » Variable

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Essay Question▾

Describe in Detail

Obtain the control limits for for the following data of 25 samples with 4 observations on the basis of volume of the bottles filled.

Given are observations find control limits for X bar Chart

Given are observations find control limits for X bar Chart

Sample No.

Observations

Sample No.

Observations

1

15.85

16.02

15.83

15.93

13

15.85

15.76

15.74

15.98

2

16.12

16.00

15.85

16.01

14

15.73

15.84

15.96

16.10

3

16.00

15.91

15.94

15.83

15

16.20

16.01

16.10

15.89

4

16.20

15.85

15.74

15.93

16

16.12

16.08

15.83

15.94

5

15.74

15.86

16.21

16.10

17

16.01

15.93

15.81

15.68

6

15.94

16.01

16.14

16.03

18

15.78

16.04

16.11

16.12

7

15.75

16.21

16.01

15.86

19

15.84

15.92

16.05

16.12

8

15.82

15.94

16.02

15.94

20

15.92

16.09

16.12

15.93

9

16.04

15.98

15.83

15.98

21

16.11

16.02

16.00

15.88

10

15.64

15.86

15.94

15.89

22

15.98

15.82

15.89

15.89

11

16.11

16.00

16.01

15.82

23

16.05

15.73

15.73

15.93

12

15.72

15.85

16.12

16.15

24

16.01

16.01

15.89

15.86

25

16.08

15.78

15.92

15.98

Explanation

From the above data we get

From the tables, for n = 4, we have

Control limits for :

And

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