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

AI and Robotics

Nov 7, 2013 (4 years and 8 months ago)

95 views

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”

Slide
2

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Bayesian Networks:

A Novel Approach

For Modelling Uncertainty in Projects

By: Vahid Khodakarami

Slide
3

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Outline:

What is missing in current PRM practice?

Bayesian Networks

Application of BNs in PRM

Models

Case study

Slide
4

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Conceptual steps in PRMP

Risk Identification

Qualitative Analysis

Risk Analysis (Risk Measurement)

Quantitative Analysis

Risk Response (Mitigation)

Slide
5

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Project Scheduling Under
uncertainty

(CPM)

PERT

Simulation

Critical chain

Slide
6

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

What is missing?

Causality

in project uncertainty

Estimation and
Subjectivity

Unknown Risks

(Common cause factors)

Trade
-
off

between time, cost and
performance

Dynamic
Learning

Slide
7

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Bayesian Networks (BNs)

Graphical model

Nodes (variables)

Arcs (causality)

Probabilistic
(Bayesian) inference

Slide
8

November 5
-
6, 2009

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

Slide
9

November 5
-
6, 2009

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

Slide
10

November 5
-
6, 2009

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

Slide
11

November 5
-
6, 2009

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

Slide
12

November 5
-
6, 2009

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)

Slide
13

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

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

Slide
14

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

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

Slide
15

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

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
   
Slide
16

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

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
Slide
17

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Activity Duration

Slide
18

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Trade off

Slide
19

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Trade off
(
Prior vs. required resources

)

Slide
20

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Known Risk

Slide
21

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Known Risk (Control)

Slide
22

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Known Risk (Impact)

Slide
23

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Known Risk (Response)

Slide
24

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Unknown Factors

Slide
25

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Unknown Factors (Learning)

Slide
26

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Learnt distribution

Slide
27

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Total Duration

Slide
28

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Case Study
(construction Project)

Slide
29

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Case Study (Bayesian CPM)

Slide
30

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Case Study (predictive)

Slide
31

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Case Study (diagnostic)

Slide
32

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Case Study (learning)

Slide
33

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

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

Slide
34

November 5
-
6, 2009

Copyright © 2009 PMI RiskSIG

Questions?

Thank you for your attention