ENG8103 – Management of technological risk

Semester 1 2015 Assignment 1

Special Instructions

1. Answer all questions, and ensure that your answers have the coverage, and are in the format, requested.

2. Present your own ideas.

3. Your answers should be properly referenced and reflect that you have undertaken research outside the study material.

4. Answers to written work are to be in Microsoft Word. Answers to numerical questions may be produced with an electronic spreadsheet, but all steps in any calculation should be clearly explained.

5. Please note that if plagiarism or cheating is detected in this assignment it will result in no marks for the assignment. Students should ensure they clearly understand the meaning of plagiarism and cheating. In particular, students should understand that while they may collaborate with other students on the conceptual ideas in their assignments, the final written report submitted by each student must be unique, and must not contain the written material of (a) any other student in the course, or (b) by any other person without due acknowledgement.

Due date: 07 September 2015

Marks: 100 Weighting: 10%

Question 1

Briefly explain the concepts of independence and dependence between two events.

(10 marks) Question 2

Consider the costs of two project items given in Fig. 2.1, with identical discrete probability distributions. They are to be linearly added.

Fig. 2.1

Item 1

Item 2

Cost ($M) Probability Cost ($M) Probability

13.0 0.150 13.0 0.150

16.5 0.600 16.5 0.600

20.0 0.250 20.0 0.250

(i) Assume independence between the two items.

1. Calculate the points of the combined probability distribution of total cost of the two items.

2. Calculate mean (expected value), variance and mode (most likely value) of the consequence of this total cost.

3. Plot the frequency distribution and cumulative probability distribution of the result.

(15 marks)

(ii) Assume complete (100%) positive dependence between the costs.

1. Calculate the points of the combined probability distribution of total cost of the two items.

2. Calculate mean (expected value), variance and mode (most likely value) of the consequence of this total cost.

3. Plot the frequency distribution and cumulative probability distribution of the result.

(15 marks)

Question 3

(i) Assuming a modified probability distribution as given in Fig. 3.1, in which the cost of the second item is conditionally dependent on the first:

1. Calculate the points of the combined probability distribution of total cost of the two items.

2. Calculate mean (expected value), variance and mode (most likely value) of the consequence of this total cost.

3. Plot the frequency distribution and cumulative probability distribution of the result.

(20 marks) Fig. 3.1

Risk 1

Risk 2

Cost ($M) Probability Cost ($M) Probability

13.0 0.150 13.0 0.350

16.5 0.650

16.5 0.600 13.0 0.200

16.5 0.550

20.0 0.250

20.0 0.250 13.0 0.050

16.5 0.800

20.0 0.150

(ii) Comment on the calculations you have made in questions 2 and 3, explaining any key points of similarity or difference between the results (up to 300 words).

(20 marks)

(iii) Discuss examples of when, in an engineering or technological project or process, you would expect to find examples of each of these three scenarios ( independence between the costs of two items, complete positive dependence between the costs of two items, and conditional dependence of the cost of one item on another) (up to 300 words).

(20 marks)

Further Information

Background reading material for this task may be found in Chapman and Ward, Chapter 11. For this question, you can consider the variables as having discrete probabilities (i.e., not continuous).

Semester 1 2015 Assignment 1

Special Instructions

1. Answer all questions, and ensure that your answers have the coverage, and are in the format, requested.

2. Present your own ideas.

3. Your answers should be properly referenced and reflect that you have undertaken research outside the study material.

4. Answers to written work are to be in Microsoft Word. Answers to numerical questions may be produced with an electronic spreadsheet, but all steps in any calculation should be clearly explained.

5. Please note that if plagiarism or cheating is detected in this assignment it will result in no marks for the assignment. Students should ensure they clearly understand the meaning of plagiarism and cheating. In particular, students should understand that while they may collaborate with other students on the conceptual ideas in their assignments, the final written report submitted by each student must be unique, and must not contain the written material of (a) any other student in the course, or (b) by any other person without due acknowledgement.

Due date: 07 September 2015

Marks: 100 Weighting: 10%

Question 1

Briefly explain the concepts of independence and dependence between two events.

(10 marks) Question 2

Consider the costs of two project items given in Fig. 2.1, with identical discrete probability distributions. They are to be linearly added.

Fig. 2.1

Item 1

Item 2

Cost ($M) Probability Cost ($M) Probability

13.0 0.150 13.0 0.150

16.5 0.600 16.5 0.600

20.0 0.250 20.0 0.250

(i) Assume independence between the two items.

1. Calculate the points of the combined probability distribution of total cost of the two items.

2. Calculate mean (expected value), variance and mode (most likely value) of the consequence of this total cost.

3. Plot the frequency distribution and cumulative probability distribution of the result.

(15 marks)

(ii) Assume complete (100%) positive dependence between the costs.

1. Calculate the points of the combined probability distribution of total cost of the two items.

2. Calculate mean (expected value), variance and mode (most likely value) of the consequence of this total cost.

3. Plot the frequency distribution and cumulative probability distribution of the result.

(15 marks)

Question 3

(i) Assuming a modified probability distribution as given in Fig. 3.1, in which the cost of the second item is conditionally dependent on the first:

1. Calculate the points of the combined probability distribution of total cost of the two items.

2. Calculate mean (expected value), variance and mode (most likely value) of the consequence of this total cost.

3. Plot the frequency distribution and cumulative probability distribution of the result.

(20 marks) Fig. 3.1

Risk 1

Risk 2

Cost ($M) Probability Cost ($M) Probability

13.0 0.150 13.0 0.350

16.5 0.650

16.5 0.600 13.0 0.200

16.5 0.550

20.0 0.250

20.0 0.250 13.0 0.050

16.5 0.800

20.0 0.150

(ii) Comment on the calculations you have made in questions 2 and 3, explaining any key points of similarity or difference between the results (up to 300 words).

(20 marks)

(iii) Discuss examples of when, in an engineering or technological project or process, you would expect to find examples of each of these three scenarios ( independence between the costs of two items, complete positive dependence between the costs of two items, and conditional dependence of the cost of one item on another) (up to 300 words).

(20 marks)

Further Information

Background reading material for this task may be found in Chapman and Ward, Chapter 11. For this question, you can consider the variables as having discrete probabilities (i.e., not continuous).

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