Answer available at:
https://drive.google.com/file/d/0B6PHuk6I5SxbSWFfRDVoLUNXMlU/view?usp=sharing
If you have a different view and feel that it may be correct than post here is as comment.
For ready reference, question is pasted here:
https://drive.google.com/file/d/0B6PHuk6I5SxbSWFfRDVoLUNXMlU/view?usp=sharing
If you have a different view and feel that it may be correct than post here is as comment.
For ready reference, question is pasted here:
Work
breakdown structure of a project is given below.
Activity
|
Immediate Predecessor
|
Expected activity time (days)
|
Activity time variance (days)^2
|
a
|
-
|
10
|
25
|
b
|
e, h
|
15
|
30
|
c
|
g, j
|
9
|
35
|
d
|
b
|
12
|
40
|
e
|
a
|
8
|
50
|
f
|
-
|
7
|
40
|
g
|
i
|
20
|
80
|
h
|
f
|
15
|
30
|
i
|
-
|
5
|
40
|
j
|
f
|
10
|
20
|
k
|
i
|
10
|
0
|
l
|
g, j, m
|
28
|
24
|
m
|
k
|
7
|
30
|
n
|
c
|
10
|
50
|
a) Draw
an activity-on-arrow network diagram and find the expected project completion
time. 2+2
marks
b) What
is the probability that this project will be completed within 65 days?
2 marks
c) A
consultant has been asked to provide his expert services in activity d. He has
been asked to report to the project office to start his work on day 52 from the
start day of the project. What is the probability that he will have to wait (i.e.
on his arrival, activity d is not ready for start)? 8 marks
d) At
present, activity g involves some human intelligence. Variance of 80 is quite
high. Suppose, this process is automated to bring the variance to 0 but the
activity time increases to 25 days. What is the probability that this changed
project will get over between 46 days and 70 days from the start of the
project?
6
marks
In part C of this question, you have taken 52 days for calculation of z value. I think it should be 51 as the consultant arrives on 52nd day and on his arrival activity D is not ready for start (for which we have to calculate the probability).
ReplyDeleteIn case of continuous variable, there may be such issues like less than equal to or equal to. Activity D doesn't start on 52nd day means its predecessors are not completed by that day.
ReplyDeleteI wouldn't be deducting marks for 51 or 52 days provided one has computed the probability of not completion of predecessor/s.
Common mistakes and marks:
ReplyDeleteSurprisingly, there are such cases in which lines are used instead of arrows in the network diagram ignoring the dependencies of the activities. In few cases, there are real activity lines/ arrows without any activity for them. Marks has to be 0 for all these.
For the consultant problem, many have answered the probability of waiting as 0 saying that 52 days is higher than the latest date of a particular event. These answers have got 0. Some have taken 37 days but used wrong path for variance or took the variance of d for calculation. They did z and probability calculations. Among them, those who subtracted the probability from 1 to get the probability to wait have been awarded 4 or 5 marks depending on clarity visible on paper. Those who have not subtracted have been awarded 2-3 marks. There is no marks deduction for calculation mistake. Taking 51 or 52 or 53 days also have made no difference in marks.
While finding the probability of project completion between 46 and 70 days, some have calculated 2 probabilities taking these values and said that the probability will lie in this range. This is escaping from the main question. Hence 1-2 marks. Some have multiplied the two probabilities or did some other things except subtracting the two. In that case 2-3 marks. Some subtracted z values and calculated probability. This is bad, hence 0 marks. Some subtracted 46 and 70, calculated z and found probability. This too is bad, hence 0.
Again, there is practically no marks deduction for calculation mistakes