November 5-6, 2009
Copyright © 2009 PMI RiskSIG
A collaboration of the
PMI, Rome Italy Chapter
and the RiskSIG
“Project Risk Management –
An International Perspective”
RiskSIG - Advancing the State of the Art
Bayesian Networks:
A Novel Approach
For Modelling Uncertainty in Projects
By: Vahid Khodakarami
November 5-6, 2009
Copyright © 2009 PMI RiskSIG
Slide 2
Outline:
 What
is missing in current PRM practice?
 Bayesian Networks
 Application of BNs in PRM
 Models
 Case study
November 5-6, 2009
Copyright © 2009 PMI RiskSIG
Slide 3
Conceptual steps in PRMP
 Risk
Identification
Qualitative Analysis
 Risk Analysis
(Risk Measurement)
Quantitative Analysis
 Risk
Response (Mitigation)
November 5-6, 2009
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Slide 4
Project Scheduling Under
uncertainty
 (CPM)
 PERT
 Simulation
 Critical
chain
November 5-6, 2009
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Slide 5
What is missing?





Causality in project uncertainty
Estimation and Subjectivity
Unknown Risks (Common cause factors)
Trade-off between time, cost and
performance
Dynamic Learning
November 5-6, 2009
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Slide 6
Bayesian Networks (BNs)

Graphical model
Nodes (variables)
Arcs (causality)

November 5-6, 2009
Probabilistic
(Bayesian) inference
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Slide 7
Bayesian vs. Frequentist
Frequentist
Bayesian
Variables
Random
Uncertain
Probability
Physical
Property
(Data)
Degree of
belief
(Subjective)
Confidence
interval
Bayes’
Theorem
Inference
November 5-6, 2009
Copyright © 2009 PMI RiskSIG
only
feasible
method for
many
practical
problems
Slide 8
Bayes’ Theorem
P( B / A)  P( A)
P( A / B) 
P( B)
 ‘A’ represents
hypothesis and ‘B’ represents
evidence.
 P(A) is called ‘prior distribution’.
 P(B/A) is called ’Likelihood function’.
 P(A/B) is called ’Posterior distribution’ .
November 5-6, 2009
Copyright © 2009 PMI RiskSIG
Slide 9
Constructing BN
Prior Probability
On time
0.95
High
0.7
Late
0.05
Low
0.3
Conditional
Probability
Sub-contract
Staff Experience
On time
High
Low
No
0.99
0.8
Yes
0.01
0.2
Late
High
Low
0.7
0.02
Delay
November 5-6, 2009
0.3
0.98
Copyright © 2009 PMI RiskSIG
Slide 10
Inference in BN
(cause to effect)
With no other information
P(Delay)=0.14.4
Knowing the sub-contract is late
P(Delay)=0.50.7
November 5-6, 2009
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Slide 11
Backward Propagation
(effect to cause)
Prior probability with no data
(0.7,0.3)
Posterior (learnt) probability
(0.28,0.72)
November 5-6, 2009
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Slide 12
BNs Advantages






Rigorous method to make formal use of subjective data
Explicitly quantify uncertainty
Make predictions with incomplete data
Reason from effect to cause as well as from cause to effect
Update previous beliefs in the light of new data (learning)
Complex sensitivity analysis
November 5-6, 2009
Copyright © 2009 PMI RiskSIG
Slide 13
BNs Applications

Industrial
 Processor Fault Diagnosis - by
Intel
 Auxiliary Turbine Diagnosis by GE
 Diagnosis of space shuttle
propulsion systems - by
NASA/Rockwell
 Situation assessment for
nuclear power plant – NRC

Medical Diagnosis
 Internal Medicine
 Pathology diagnosis  Breast Cancer Manager
November 5-6, 2009

Commercial
 Software troubleshooting and
advice – MS-Office
 Financial Market Analysis
 Information Retrieval
 Software Defect detection

Military
 Automatic Target Recognition
– MITRE
 Autonomous control of
unmanned underwater vehicle
- Lockheed Martin
Copyright © 2009 PMI RiskSIG
Slide 14
Bayesian CPM
CPM Calculation
ES  Max[EFj | j one of the predecessor activities ]
EF  ES  D
LS  LF  D
LF  Min[LS j | j one of the successor activities ]
Slack  LS  ES  LF  EF
Predecessors
Duration
Model
Predecessor
Activities
D
ES
LS
EF
Successor
Activities
Successors
November 5-6, 2009
LF
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Slide 15
BCPM Example
ES=5
ES=0
D=5
D=4
EF=9
ES=9
D=2
EF=11
B
D
LS=9 Slack=4 LF=13
LS=13 Slack=4 LF=15
EF=5
ES=15
D=5
EF=20
A
E
LS=0 Slack=0 LF=5
LS=15 Slack=0 LF=20
ES=5
D=10
EF=15
C
LS=5 Slack=0 LF=15
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Slide 16
Activity Duration
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Slide 17
Trade off
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Slide 18
Trade off
November 5-6, 2009
(Prior vs. required resources )
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Slide 19
Known Risk
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Slide 20
Known Risk (Control)
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Slide 21
Known Risk (Impact)
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Slide 22
Known Risk (Response)
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Slide 23
Unknown Factors
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Slide 24
Unknown Factors (Learning)
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Slide 25
Learnt distribution
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Slide 26
Total Duration
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Slide 27
Case Study (construction Project)
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Slide 28
Case Study (Bayesian CPM)
November 5-6, 2009
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Slide 29
Case Study (predictive)
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Slide 30
Case Study (diagnostic)
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Slide 31
Case Study (learning)
November 5-6, 2009
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Slide 32
Summary
 Current
practice in modelling risk in project
time management has serious limitations
 BNs are particularly suitable for modelling
uncertainty in project
 The proposed models provide a new
generation of project risk assessment tools
that are better informed and hence, more
valid
November 5-6, 2009
Copyright © 2009 PMI RiskSIG
Slide 33
Questions?
Thank you for your attention
November 5-6, 2009
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Slide 34