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MLA

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Accounting, Finance, SPSS

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Math Problem

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English (U.S.)

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# Quantative Techniques: Solve Math Problems and Draw Charts (Math Problem Sample)

Instructions:

Solve math problems and draw charts

source..Content:

Name

Professor

Subject

Date

QUESTION ONE

The product delivery system is a series-parallel system. The state function that is used to assess the reliability of the system is by decomposing the system into respective sub-systems.

The parallel sub-system reliability calculation is through co- product of the individual elements

The parallel subsystem contains two components with identical reliability of (1 â€“ 3/10,000)

Individual reliability = 0.9997

Subsystem reliability R= 1 â€“ (1 â€“ 0.9997)2 = 0.9999

The series sub-system reliability calculation is through product of individual reliabilities

The 15 components in the series sub-system each with a reliability of (1 â€“ 1/10,000)

Individual component reliability = 0.9999

Reliability of the sub-system = (0.9999)15

R = 0.9985

Finally, since the two subsystems are put together in series, the overall reliability is the product of the two sub-systems, (0.9999 . 0.9985) = 0.9985

QUESTION TWO

The Xbar - chart shown in the plot below evaluates the consistency of sample averages by graphing the average of each sample. It is useful at showing the relatively large deviations in the plotted sample average.

The R-chart plots the ranges of each sample. The R chart evaluates the consistency of sample variation

Answer: The Xbar - chart and R-chart plots

The process is not under control since there exist some relatively large deviations in the sample range. Sample 6, 7 and 8 are out of control.

QUESTION THREE

Data Table

Type of Problem

Frequency

CUMULATIVE TOTAL

CUMULATIVE TOTAL

Batteries not included

21

21

42%

Items damaged when received

13

34

68%

Literature is not included in box

9

43

86%

Parts missing

6

49

98%

Unit not working

1

50

100%

Answer: Pareto chart with cumulative % frequency

The cumulative frequency of the two left-most bars is 68%.

QUESTION FOUR

Answer: Mean and standard deviation

Customer

Satisfaction rating

1

4

2

3

3

2

4

5

5

5

6

2

7

1

8

4

9

3

10

4

11

4

12

5

13

3

14

3

15

2

16

1

17

5

18

3

19

4

20

3

21

4

22

2

23

4

24

4

25

3

26

3

27

3

28

2

29

2

30

3

...

Professor

Subject

Date

QUESTION ONE

The product delivery system is a series-parallel system. The state function that is used to assess the reliability of the system is by decomposing the system into respective sub-systems.

The parallel sub-system reliability calculation is through co- product of the individual elements

The parallel subsystem contains two components with identical reliability of (1 â€“ 3/10,000)

Individual reliability = 0.9997

Subsystem reliability R= 1 â€“ (1 â€“ 0.9997)2 = 0.9999

The series sub-system reliability calculation is through product of individual reliabilities

The 15 components in the series sub-system each with a reliability of (1 â€“ 1/10,000)

Individual component reliability = 0.9999

Reliability of the sub-system = (0.9999)15

R = 0.9985

Finally, since the two subsystems are put together in series, the overall reliability is the product of the two sub-systems, (0.9999 . 0.9985) = 0.9985

QUESTION TWO

The Xbar - chart shown in the plot below evaluates the consistency of sample averages by graphing the average of each sample. It is useful at showing the relatively large deviations in the plotted sample average.

The R-chart plots the ranges of each sample. The R chart evaluates the consistency of sample variation

Answer: The Xbar - chart and R-chart plots

The process is not under control since there exist some relatively large deviations in the sample range. Sample 6, 7 and 8 are out of control.

QUESTION THREE

Data Table

Type of Problem

Frequency

CUMULATIVE TOTAL

CUMULATIVE TOTAL

Batteries not included

21

21

42%

Items damaged when received

13

34

68%

Literature is not included in box

9

43

86%

Parts missing

6

49

98%

Unit not working

1

50

100%

Answer: Pareto chart with cumulative % frequency

The cumulative frequency of the two left-most bars is 68%.

QUESTION FOUR

Answer: Mean and standard deviation

Customer

Satisfaction rating

1

4

2

3

3

2

4

5

5

5

6

2

7

1

8

4

9

3

10

4

11

4

12

5

13

3

14

3

15

2

16

1

17

5

18

3

19

4

20

3

21

4

22

2

23

4

24

4

25

3

26

3

27

3

28

2

29

2

30

3

...

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