The standard deviation is the square root of the variance, which is 1.465 weeks. Z = (Target Time - Expected Time) / Standard Deviation = (42 - 40) / 1.465 = 1.37 Looking up 1.37 in the standard normal distribution table gives a probability of around 0.085 or 8.5% that the project will take longer than 42 days.

1. Engineering Mangement
Program Evaluation Review
Technique (PERT)
Prepared by :
Anas Tomeh Fira Eid
Prepared for :
Dr. Reema Nassar

2. Objective of the presentation
• To understand the formula , the use and
the benefits of Program , Evaluation ,and
Review Technic (PERT) analysis .

3. What is the PERT ?
Program (Project) Evaluation and Review Technique (PERT): is
a project management tool used to schedule, organize, and
coordinate tasks within a project. It is basically a method to
analyse the tasks involved in completing a given
project, especially the time needed to complete each task, and
to identify the minimum time needed to complete the total
project.

4. When we use PERT ?
• PERT is used when activity times are uncertain.
– Determine the duration of the project .
– Decision making under risk (“P” for probabilistic)

5. Determine the duration of the project
• OPTIMISTIC TIME: Best time if everything goes perfectly
• REALISTIC TIME: Most likely time
• PESSIMISTIC TIME: A worst-case situation
B + 4M + P
Expected Time = -------------------
6

6. Determine the duration of the project
• Example:
For excavation activity let :
B = 12 days
M = 18 days
P = 60
What is the expected time for this activity?
Sol :
12 + 4(18) + 60
Expected Time = -------------------------
6
= 24 days

7. Determine the duration of the project
Activity Predecessor Optimistic Normal Pessimistic Te
(B) (m) (P) (B+4m+P)/6
A --- 2 4 6 4.00
B --- 3 5 9 5.33
C A 4 5 7 5.17
D A 4 6 10 6.33
E B, C 4 5 7 5.17
F D 3 4 8 4.50
G E 3 5 8 5.17
f

8. Determine the duration of the project
D F
A
C
Start Finish
B E G

9. Determine the duration of the project
D F
D:6.33 D:4.5
ES:4 ES:10.33
EF:10.33 EF:14.83
A
D:4
ES:0
EF:4
C
D:5.17 Finish
Start ES:4
ES:0 D:0
EF:9.17 ES:19.51
EF:0
EF:19.51
B E G
D:5.33 D:5.17 D:5.17
ES:0 ES:9.17 ES:14.34
EF:5.33 EF:14.34 EF:19.51

10. Determine the duration of the project
D F
D:6.33 D:4.5
ES:4 ES:10.33
EF:10.33 EF:14.83
LS:8.68 LS:15.01
LF:15.01 LF:19.51
A
D:4
ES:0
EF:4
LS:0
LF:4
C
D:5.17
Start Finish
ES:4
D:0 D:0
EF:9.17
ES:0 ES:19.51
LS:4
EF:0 EF:19.51
LF:9.17
LS:0 LS:19.51
LF:0 LF:19.51
B E G
D:5.33 D:5.17 D:5.17
ES:0 ES:9.17 ES:14.34
EF:5.33 EF:14.34 EF:19.51
LS:3.84 LS:9.17 LS:14.34
LF:9.17 LF:14.34 LF:19.51

11. Determine the duration of the project
Critical Path
Critical Path: A-C-E-G
• Path A-D-F = 14.83 work days
• Path A-C-E-G = 19.51 work days
• Path B-E-G = 15.67 work days

12. Determine the duration of the project
Critical Path
Activity LF-EF Total
A 4-4 0
B 9.17 – 5.33 3.84
C 9.17 – 9.17 0
D 15.01 – 10.33 4.68
E 14.34 – 14.34 0
F 19.51 – 14.83 4.68
G 19.51 – 19.51 0

13. Assessing Risks
• Risk is a measure of the probability (and
consequences) of not completing a project
on time.
• A major responsibility of the project
manager at the start of a project is to
develop a risk-management plan.
• A Risk-Management Plan identifies the
key risks to a project’s success and
prescribes ways to circumvent them.

14. Assessing Risks
• With PERT’s three time-estimates, we get a mean
(average) time and a variance for each activity and each
path.
– We also get a project mean time and variance.
• In order to compute probabilities (assuming a normal
distribution) we need the activity means and variances.
– Most computer packages calculate this for you.

15. Assessing Risks
Path Time (wks) 12
I 27
48 1563
A-I-K33 33
A-F-K28 28
A K
A-C-G-J-K 67 0 12 12 F 22 Latest 63 69 Latest
B-D-H-J-K 69 2 1214 53 1063 start 63 6 69
finish
B-E-J-K 43 time time
C
12 22 22 G 57
Start Finish
14 1024 24 59
35
0
B9 9
D19 19
H 59 59
J 63
0 9 9 9 1019 19 4059 59 4 63
9 E 33
35 2459

16. Assessing Risks
• What is the probability that our sample project
will finish in 69 weeks as scheduled?
100% (Why?)
– Because we used CPM!
• (This means we were certain of all of our activity times.)
– If we weren’t certain, we should have used PERT
• You can’t do risk analysis if you use CPM

17. Assessing Risks
• Calculate standard deviation
– Standard deviation- average deviation from the
estimated time
• SD=(TP-T0)/6
– higher the SD is the greater amount of uncertainty
exists
• Calculate variance
– reflects the spread of a value over a normal
distribution
• V=SD2
– a large variance indicates great uncertainty, a small
variance indicates a more accurate estimate

18. Assessing Risks
What is the Probability of it taking 72 weeks?
Critical Critical Path = B - D - H - J – K = 69 weeks
Path T = 72 weeks C = 69 weeks
Varianc T–C
e
2 =  (variances of activities along critical path) =
z
2
2 = 1.78 + 1.78 + 2.78 + 5.44 + 0.11 = 11.89
z= 72 – 69
11.89 Look up Z value in normal distribution table
Z = 0.870 Pz = .8078 or 80.78%
(Probability of it taking 72 weeks)

19. Assessing Risks
Look up the Z value (0.870) in the table of normal distribution.
.8078 or 80.78% is the probability of the project taking up to 72 wks.
Going over 72 weeks would be 100 – 80.78 = 19.22%

20. Assessing Risks
Normal distribution:
Length of critical Mean = 69 weeks;
path is 69 weeks  = 3.45 weeks
Probability of taking
72 weeks is 0.8078 Probability of
or 80.78% exceeding 72 weeks
is 0.1922 or 19.22%
69 72
Project duration (weeks)

21. Assessing Risks
• Assume a PERT project critical path takes 40 days, and that the
variance of this path is 2.147
– You wish to know the probability of the project going over 42 days.
• Compute the standard deviation of the critical path. (Take the square
root of the variance of 2.147) Std. Dev. = 1.465
– POM/QM software gives you the variance of the critical path.
• Compute the Z value: Z = (absolute time difference) / Std. Dev.
In this example, Z = (42 days - 40 days) / 1.465 = 1.365
• Look up the Z value of 1.365 in a Normal Distribution table to get the
probability of the project taking 42 days.
• Subtract it from 100% to get the probability of going over 42.

22. Assessing Risks
Look up the Z value (1.365) in the table of normal distribution.
(In this case you need to interpolate between the Z values of .9313 and .9147)
.9139 or 91.39% is the probability of the project taking up to 42 days.
Going over 42 days is thus 100 - 91.39 = 8.61%

23. Thank you for attention
Any Questions ????