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Copyright © 2009 PMI RiskSIGNovember 5-6, 2009
RiskSIG - Advancing the State of the ArtRiskSIG - Advancing the State of the Art
A collaboration of theA collaboration of the PMI, Rome Italy Chapter PMI, Rome Italy Chapter
and the RiskSIGand the RiskSIG
““Project Risk Management – Project Risk Management – An International An International
Perspective”Perspective”
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Copyright © 2009 PMI RiskSIG Slide 2November 5-6, 2009
Bayesian Networks:
A Novel Approach
For Modelling Uncertainty in Projects
By: Vahid Khodakarami
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Copyright © 2009 PMI RiskSIG Slide 3November 5-6, 2009
Outline:
What is missing in current PRM practice? Bayesian Networks Application of BNs in PRM Models Case study
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Copyright © 2009 PMI RiskSIG Slide 4November 5-6, 2009
Conceptual steps in PRMP
Risk IdentificationQualitative Analysis
Risk Analysis (Risk Measurement)Quantitative Analysis
Risk Response (Mitigation)
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Copyright © 2009 PMI RiskSIG Slide 5November 5-6, 2009
Project Scheduling Under uncertainty
(CPM) PERT Simulation Critical chain
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Copyright © 2009 PMI RiskSIG Slide 6November 5-6, 2009
What is missing?
Causality in project uncertainty Estimation and Subjectivity Unknown Risks (Common cause factors) Trade-off between time, cost and
performance Dynamic Learning
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Copyright © 2009 PMI RiskSIG Slide 7November 5-6, 2009
Bayesian Networks (BNs)
Graphical modelNodes (variables)Arcs (causality)
Probabilistic (Bayesian) inference
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Copyright © 2009 PMI RiskSIG Slide 8November 5-6, 2009
Bayesian vs. Frequentist
Frequentist Bayesian
Variables Random Uncertain
Probability
Physical Property
(Data)
Degree of belief (Subjective)
Inference Confidence interval
Bayes’ Theorem
only feasible
method for many
practical problems
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Copyright © 2009 PMI RiskSIG Slide 9November 5-6, 2009
Bayes’ Theorem
‘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’ .
( / ) ( )( / )
( )
P B A P AP A B
P B
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Copyright © 2009 PMI RiskSIG Slide 10November 5-6, 2009
Constructing BN
High 0.7
Low 0.3
On time 0.95
Late 0.05
Prior Probability
Sub-contract On time Late
Staff Experience High Low High Low No 0.99 0.8 0.7 0.02Delay Yes 0.01 0.2 0.3 0.98
Conditional Probability
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Copyright © 2009 PMI RiskSIG Slide 11November 5-6, 2009
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
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Copyright © 2009 PMI RiskSIG Slide 12November 5-6, 2009
Backward Propagation(effect to cause)
Prior probability with no data
(0.7,0.3)
Posterior (learnt) probability
(0.28,0.72)
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Copyright © 2009 PMI RiskSIG Slide 13November 5-6, 2009
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
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Copyright © 2009 PMI RiskSIG Slide 14November 5-6, 2009
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
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
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Copyright © 2009 PMI RiskSIG Slide 15November 5-6, 2009
Bayesian CPM
ES
D
EFLF
LS
PredecessorActivities
SuccessorActivities
Su
ccesso
rs
Pred
ecesso
rs
Duration Model
CPM Calculation[ j ]jES Max EF one of the predecessor activities |
EF ES D
LS LF D
[ j ]jLF Min LS one of the successor activities | Slack LS ES LF EF
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Copyright © 2009 PMI RiskSIG Slide 16November 5-6, 2009
BCPM Example
D=5 EF=5
LS=0 Slack=0 LF=5
ES=0
A
D=4 EF=9
LS=9 Slack=4 LF=13
ES=5
B
D=10 EF=15
LS=5 Slack=0 LF=15
ES=5
C
D=2 EF=11
LS=13 Slack=4 LF=15
ES=9
D
D=5 EF=20
LS=15 Slack=0 LF=20
ES=15
E
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Activity Duration
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Trade off
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Trade off (Prior vs. required resources )
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Known Risk
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Known Risk (Control)
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Known Risk (Impact)
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Known Risk (Response)
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Unknown Factors
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Unknown Factors (Learning)
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Learnt distribution
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Total Duration
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Case Study (construction Project)
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Case Study (Bayesian CPM)
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Case Study (predictive)
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Copyright © 2009 PMI RiskSIG Slide 31November 5-6, 2009
Case Study (diagnostic)
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Case Study (learning)
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Copyright © 2009 PMI RiskSIG Slide 33November 5-6, 2009
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
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Copyright © 2009 PMI RiskSIG Slide 34November 5-6, 2009
Questions?
Thank you for your attention