Durations

fable F. 10 Calculating expected activity durations

Activity durations (weeks) Activity Optimistic (a) Most likely (m) Pessimistic (/>) Expected (f,)

A

5

6

8

6.17

B

3

4

5

4.00

C

2

3

3

2.83

D

3.5

4

5

4.08

E

1

3

4

2.83

F

8

10

15

10.50

i ém

3

4

3.00

II

2

-> ém

2.5

2.08

7.5 The forward pass to calculate expected completion date

The expected duration and the expected dates for the other project events are shown in Figure 7.3. An expected duration of 13.5 weeks means that we expect the project to be completed half way through week 14. although since this is only an expected value it could tinish earlier or later.

7.6 Calculating standard deviations

The correct values are show n in Figure 7.4. Brief calculations for events 4 and 6 are given here.

Event 4: Path A + C has a standard deviation of V(0.50*+ 0.17:) = 0.53 Path B + I) has a standard deviation of V(0.33;+ 0.251) = 0.41 Node 4 therefore has a standard deviation of 0.53.

Event 6: Path 4 + H has a standard deviation of V<0.53'+ 0.08') = 0.54 Path 5 + G has a standard deviation of \( 1. 17:+ 0.332) = 1.22 Node 6 therefore has a standard deviation of 1.22.

7.7 Calculating z values

TK If .<• 10-10.5 nor 15-13.5 . I he value for event 5 is ———— = -0.43 . for event 6 it is —t-tt— = 1.23

1.17

7.8 Obtaining probabilities

Event 4: The ; value is 1.89 which equates to a probability of approximately 3%. There is therefore only a 3% chance that we w ill not achieve this event by the target date of the end of week 10. Event 5: The c value is -0.43 which equates to a probability of approximately 67%. There is therefore a 68% chance that we w ill not achieve this event by the target date of the end of week 10.

To calculate the probability of completing the project by week 14 we need to calculate a new z value for event 6 using a target date of 14. This new ; value is

This equates to a probability of approximately 35%. This is the probability of not meeting the target date. The probability of meeting the target date is therefore 65% (100% -35%).

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