PERT

1. SPM-UNIT III
RISK MANAGEMENT
Prof. Kanchana Devi

2. PERT Technique
 Used to evaluate the effects of uncertainty
 CPM & PERT are similar
 CPM requires Single Estimate
 PERT requires Three Estimates
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3. PERT Three Estimates are
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 Most Likely Time
 The time we would expect the task to take under
normal circumstances.“ m”
 Optimistic Time
 Shortest time in which we could expect to complete
the activity, barring the miracles.“a”
 Pessimistic Time
 Worst Possible time. “b”

4. Expected Duration
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 PERT Combines the three estimates to form a
single expected duration, te
 Formula for te is
te= a+4m+b
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5. Calculate the expected duration
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Activity Optimistic(a) Most Likely(m)
Activity Duration
Pessimistic(b)
A 5 6 8
B 3 4 5
C 2 3 3
D 3.5 4 5
E 1 3 4
F 8 10 15
G 2 3 4
H 2 2 2.5

6. After Calculating Expected
Duration
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7. PERT Network after the
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8. Activity Standard Deviation
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 S = b-a which gives the degree of uncertainty
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 The activity standard deviation is proportional to
the difference between the optimistic and
pessimistic estimates.
 Can be used as a ranking measure of the degree of
uncertainty or risk for each activity

9. Standard Deviation
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10. PERT With ‘SD’
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11. Probability of Meeting or Missing
Target Date
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 The PERT Technique uses the following three
step method for calculating the probability
of meeting or missing a target date:
 Calculate SD of each project event
 Calculate the Z value for each event that has a target
value
 Convert Z values to a probability

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 Note: To add two Standard Deviations we
must add their squares and then find the
square root of the sum.
 The SD for event 3 depends on the activity B.
The SD for event 3 is therefore 0.33
 For event 5 there are two possible paths, B+E
or F. The total SD for path B+E is
√(0.332+0.502) = 0.6 and For path F is 1.17
 SD for event 5 is therefore the greater of two
1.17

13. Z- Value Formula
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 Te  is the Expected Date
 T  Target Date
 S  SD
Z = T - te
S

14. Calculate Z value –Event ‘4’
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 (10-9.00)/0.53 = 1.8867
 A Z-Value may be converted to the
probability of not meeting the target date by
using the graph given below

15. Converting Z values to
Probabilities
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 A Z-value may be converted to the
probability of not meeting the target date by
using the graph.
 Eg:
 The Z-Value for the project completion (event 6)
is 1.23. Using graph this equates to a probability
of approximately 11%, that is, there is an 11%
risk of not meeting the target date of the end of
week 15.

16. Monte Carlo Simulation
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 An alternative to PERT Technique
 MC Simulation are a class of general analysis
techniques that are valuable to solve any
problem that is complex, nonlinear or for some
uncertain parameters.
 It involves repeated random sampling to
compute the results.
 Advantage:
 Repeated computation of random numbers - easier
to use this technique when available as a computer
program

17. Steps – MC Simulation
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 Step 1: Express the project completion time in terms of the
duration of the n-activities xi,i=1,n and their dependencies
as a precedence graph, d= f(x1,x2,….xn).
 Step 2: Generate a set of random inputs, Xi1,Xi2, …Xin using
the specified probability distributions.
 Step 3: Evaluate the project completion time expression
and store the result in di.
 Step 4: Repeat steps 2 and 3 for the specified number of
times.
 Step 5: Analyze the results di, i=1,n; summarize and display
using a histogram.

18. Histogram
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