Bayesian Networks: a Novel Approach for Modelling Risk and ...

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Copyright © 2009 PMI RiskSIG

November 5
-
6, 2009

RiskSIG
-

Advancing the State of the Art

A collaboration of the


PMI, Rome Italy Chapter

and the RiskSIG

“Project Risk Management



An International Perspective”

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Copyright © 2009 PMI RiskSIG


Bayesian Networks:


A Novel Approach

For Modelling Uncertainty in Projects



By: Vahid Khodakarami

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November 5
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Copyright © 2009 PMI RiskSIG

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

Conceptual steps in PRMP



Risk Identification


Qualitative Analysis


Risk Analysis (Risk Measurement)


Quantitative Analysis


Risk Response (Mitigation)


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Project Scheduling Under
uncertainty



(CPM)


PERT


Simulation


Critical chain


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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

Bayesian Networks (BNs)



Graphical model


Nodes (variables)


Arcs (causality)



Probabilistic
(Bayesian) inference

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Copyright © 2009 PMI RiskSIG

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

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 A
P A B
P B


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Copyright © 2009 PMI RiskSIG

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 0.02

Delay


Yes 0.01 0.2 0.3 0.98




Conditional

Probability

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Copyright © 2009 PMI RiskSIG

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

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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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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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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Bayesian CPM

ES
D
EF
LF
LS
Predecessor
Activities
Successor
Activities
Successors
Predecessors
Duration
Model
CPM Calculation

[ j ]
j
ES Max EF one of the predecessor activities

|
EF ES D
 
LS LF D
 
[ j ]
j
LF Min LS one of the successor activities

|
Slack LS ES LF EF
   
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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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Case Study (diagnostic)

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Case Study (learning)

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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

Questions?




Thank you for your attention