Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
1
Bayesian networks applications in dependability
Philippe WEBER
Centre de Rechercheen Automatiquede Nancy (CRAN),
UMR 7039 CNRS Nancy Université
2, rue Jean LamourF54519 VandoeuvrelèsNancyCedex–France
Email: [philippe.weber@cran.uhpnancy.fr]
All our papers are available on HAL
http://hal.archivesouvertes.fr
Simple Search : «philippeweber»; Author (first lastname)
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Static
Bayesian
Bayesian
Networks
Networks
models
models
Dynamic
Bayesian
Bayesian
Networks
Networks
models
models
******
******
Applications
Water heater systemReliability
Risk analysis of sociotechnical system
*******
Conclusion
Outline
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Static Bayesian Network model
(
)
(
)
(
)
()
()
downXpdownX1 StateXp
upXpupX1 StateXp 1 StateXp
=⋅==+
=⋅====
112
1122
The marginal probability X2
is computed as follows
(
)
22.08.01.02.00
2
=
⋅
+
⋅
=
=.7 1 StateXp
Component states
X1
X2
knowledge
With the a priori knowledge
X
1
updown
0.20.8
X
2
State 1State 2State 3
up0.70.10.2
down0.10.60.3
X
1
Conditional Probability Table
CPT
p(X2X1)?
Discrete
random
variable
variable states
a priori distribution
failure modes
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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X
1
updown
0.20.8
X
2
State 1State 2State 3
up0.70.10.2
down0.10.60.3
X
1
Conditional Probability Table
CPT
p(X2X1)?
Discrete
random
variable
variable states
The marginal probability X1
is computed with the Bayestheorem
The propagation of this probability through the BN is based on
inferencealgorithms
X1
X2
knowledge
()
(
)
()
()
1 StateX
X1 StateXX
1 StateXX
2
121
21
=
==⋅=
===
p
uppupp
upp
a priori distribution
Static Bayesian Network model
Component states
failure modes
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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X0
p(X1  X0)
State 1State 2
State 10.60.4
State 20.80.2
p(X2
 X1)
p(X1)
updown
0.10.9
p(X0)
p(X0)
State 1State 2
up
0.10.9
down
0.70.3
X1
X2
Static Bayesian Network model
Impacts on the system
Component
states
Failure
modes
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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p(X
2
 X1)
p(X1)
p
(X
(X2
2=state1)=0.7*0.6+0.3*0.8=
=state1)=0.7*0.6+0.3*0.8=
0.66
0.66
p
(X
(X2
2=state2)=0.7*0.4+0.3*0.2=
=state2)=0.7*0.4+0.3*0.2=
0.34
0.34
updown
01
Hard evidence
Hard evidence
p(X1  X0)
p(X0)
p(X0)
1
1
0
0
1
1
0
0
1
1
0
0
X0
X1
X2
State 1State 2
up
0.10.9
down
0.70.3
State 1State 2
State 10.60.4
State 20.80.2
p
(X
(X
1
1
=state1)=
=state1)=
0.7
0.7
p
(X
(X
1
1
=state2)=
=state2)=
0.3
0.3
Static Bayesian Network model
System
Component
states
Failure
modes
Impacts on the system
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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p(X2)
updown
01
Hard evidence
Hard evidence
p(X1  X0)
p(X0)
p(X0)
1
1
0
0
1
1
0
0
X0
X1
X2
State 1State 2
up
0.10.9
down
0.70.3
State 1State 2
01
Hard evidence
Hard evidence
1
1
0
0
p
(X
(X
1
1
=state1)=
=state1)=
0.8235
0.8235
p
(X
(X
1
1
=state2)=
=state2)=
0.1765
0.1765
Static Bayesian Network model
System
Component
states
Failure
modes
Impacts on the system
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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p(X2)
updown
01
Hard evidence
Hard evidence
p(X1  X0)
p(X0)
p(X0)
1
1
0
0
1
1
0
0
X0
X1
X2
State 1State 2
up
0.10.9
down
0.70.3
State 1State 2
0.20.8
soft evidence
soft evidence
1
1
0
0
p
(X
(X
1
1
=state1)=
=state1)=
0.78
0.78
p
(X
(X
1
1
=state2)=
=state2)=
0.22
0.22
Static Bayesian Network model
System
Component
states
Failure
modes
Impacts on the system
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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StaticBayesian Networks generalized
Fault Tree and Reliability Diagram
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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A) Parallel Architecture
()()()
RB
i
i
OKSpHSFpSp===−=
∏
=
3
2
1
1
F1=
F1=
HS
HS
F2=
F2=
HS
HS
ER
ER
S
S
3
3
=
=
HS
HS
Reliability Diagram
Fault Tree
Reliability model of a system with 2 components (the variables have 2 states : OK or HS)
StaticBayesian Networks generalized Fault Tree and Reliability Diagram
Bayesian network
Static Bayesian Network model
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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()()()
RB
i
i
OKSpOKFpSp====
∏
=
3
2
1
F1=
F1=
HS
HS
F2=
F2=
HS
HS
ER
ER
S
S
3
3
=
=
HS
HS
B) Serial Architecture
Bayesian network
Reliability Diagram
Fault Tree
Reliability model of a system with 2 components (the variables have 2 states : OK or HS)
StaticBayesian Networks generalized Fault Tree and Reliability Diagram
Static Bayesian Network model
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Complex system reliability model
CMP1
CMP2
CMP3
CMP4
CMP5
To model the reliability of this system a tree
is not adapted because it is not possible to
factorized CMP1, CMP2 and CMP5
Using BN the model is formalized as a
Directed Acyclic Graph (DAG)
The computations are based on inference
algorithms
TopEvent=
CMP3.CMP4
+CMP1.CMP2
+CMP1.CMP5.CMP4
+CMP2.CMP5.CMP3
StaticBayesian Networks generalized Fault Tree and Reliability Diagram
Static Bayesian Network model
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Modeling real problem the variables are not Boolean ! The components
may be affected by several failures. The reliability model of this system
can not be solve using Fault tree model
The BN is directly used to formalized the equation in the CPT with multimodal
variable F2
Multimodal Variables
StaticBayesian Networks generalized Fault Tree and Reliability Diagram
Static Bayesian Network model
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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The model structure of the GRAPH allows dependency
and multimodal variables
Multimodal Variables
StaticBayesian Networks generalized Fault Tree and Reliability Diagram
Static Bayesian Network model
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Dynamic
Bayesian
Bayesian
Networks
Networks
models
models
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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System reliability
)(tRS
The probability that no failure occurred during the interval [
0, t]
)(t
S
λ
Failure rate of the systemat time t
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−=
∫
t
SS
dtttR
0
)(exp)(
λ
DynamicBayesianNetworks in SystemReliabilityAnalysis
The probability that a failure occurred between
t
and t+dt
is
approximated by
When the system is composed with several components
Then the failure rate is defined for each component
)(t
n
λ
摴tp
nn
⋅
=
)(
λ
Markov Chain is a classic solution to model this sort of
system Reliability when failure rates are constant
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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2
2
Time
Time
slices
slices
A Dynamic Bayesian Network (DBN)
is a BN extension
including temporal dimensionality
Red arcs represent the temporal
dependence between differenttime
slices
Defining these impacts as transition
probabilitiesbetween the states of the
variable X at time (k1) and (k)
The DBN compute the behaviour of
the probability distribution over the
stats of the variable X
X(k)updown
up
0.90.1
down
01
X(k1)
X(k1)
X(k)
intertimeslices CPT
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Then the intertime slices CPT
is a Markov Chain model
Starting from an observed situation at time k=0, the probability
distribution over the states at the next timeis computed
using successive inferences
(the variable Xk
is considered as the new observation of X
k1
through a
time feedback)
a time feedback
a time feedback
intertime slices CPT
X(k)updown
up
0.90.1
down
01
X(k1)
X(k1)X(k)
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Then the reliability is given by simulation
Dynamic
Bayesian Network / Markov Chain model
Bayesian Network / Markov Chain model
))(()(upkXPkR
n
=
=
WEBER P., JOUFFE L. Reliability modelling with Dynamic Bayesian Networks. 5th IFAC
Symposium on Fault Detection, Supervision and Safety of Technical Processes
(SAFEPROCESS'03), Washington, D.C., USA, 911 juin, 2003.
M
TTF
n
1
=
λ
tp
n
∆
≅
λ
12
X(k)updown
up
1
p
12
p
12
down
01
X(k1)
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Dynamic
Bayesian Network / semi Markov Process
Bayesian Network / semi Markov Process
))(()(upkXPkRn
=
=
System with time variant failure rate
System with time variant failure rate
(
(
weibull
weibull
)
)
The parameter in the CPT
The parameter in the CPT
are indexed by time
are indexed by time
50,5.2,)(
1
1
==
⋅
=
−
ηβ
η
β
λ
β
β
t
t
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Markov Switching Model
Markov Switching Model
Dynamic
Bayesian Network / Markov Switching Model
Bayesian Network / Markov Switching Model
A process changes its behavior according to the state of
A process changes its behavior according to the state of
exogenous constraints representing functioning conditions,
exogenous constraints representing functioning conditions,
maintenance events
maintenance events
…
…
The exogenous constraint is represented by an external variable
The exogenous constraint is represented by an external variable
U
U
k
k
U(k)=
U(k)=
α
α
U(k)=
U(k)=
β
β
OK
f
)(
1
α
=
λ
f
OK
f
)(
1
β
=
λ
f
)(
MCt
T
t
X
dt
dX
PI−⋅=
⎥
⎦
⎤
⎢
⎣
⎡
Analytic solution
Analytic solution
Discret
Discret
simulation
simulation
WEBER P., MUNTEANU P., JOUFFE L. Dynamic Bayesian Networks modelling the dependability of systems with degradations and exogenous constraints. 11th
IFAC Symposium on Information Control Problems in Manufacturing,INCOM'04. SalvadorBahia, Brazil, April 57th, (2004).
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Dynamic
Bayesian Network / Markov Switching Model
Bayesian Network / Markov Switching Model
))(()(upkXPkRn
=
=
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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X(k1)X(k)
U(k1)
Y(k)
Hidden Process
Observations
Dynamic
Bayesian Network / IOHMM
Bayesian Network / IOHMM
In the previous slides the stochastic processes are supposed to be
completely observable. In practice this is seldom the reality
because the physical degradations of a component result in a
change of its state which is observed only through a variation in
the component functionality.
Parameter estimation needs many data !!!
Parameter estimation needs many data !!!
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Dynamic
Bayesian Network
Bayesian Network


Factorized MC model
Factorized MC model
The reliability of component can be modelled as a DBN as presented before
If the components are independent the DBN allows to merge the models
through a factorised form
X1(k1)
X1(k)
U(k1)
Y3(k)
X2(k1)
X2(k)
X3(k1)
X3(k)
Y2(k)
Y1(k)
IOHMM
X2(k2)
Markov
Markov2
2
1/2Markov
1/2Markov
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Dynamic Bayesian Network
Dynamic Bayesian Network


Factorized MC model
Factorized MC model
The reliability of component can be modelled as a DBN as presented before
If the components are independent the DBN allows to merge the models
through a factorised form
X1(k1)
X1(k)
U(k1)
Y3(k)
X2(k1)
X2(k)
X3(k1)
X3(k)
Y2(k)
Y1(k)
IOHMM
X2(k2)
Markov
Markov2
2
1/2Markov
1/2Markov
S(k)
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Applications
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Process modelling approach in real application
Process modelling approach in real application
•Methodology
–Process and flowbased approach
•Functional/Dysfunctional reasoning
•Hierarchical structure
–Elaboration of the probabilistic network
•Formalism: BN/DBN
•Generic rules to transform the process
model into a probabilistic one
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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To Control
To transform
To measure
PLC
Sensor
Machine
Position order
input productfinished product
finished product
Product report
Process modelling approach in real application
Process modelling approach in real application
DynamicBayesianNetworks in SystemReliabilityAnalysis
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
29
To measure
To Control
To transform
PLC
Sensor
Machine
Order
(k+1)
input product(k)
finishedproduct
(k+1)
finishedproduct
(k)
Productreport
Time
(k+1)
DynamicBayesianNetworks in SystemReliabilityAnalysis
Process modelling approach in real application
Process modelling approach in real application
(
(Time formalisation)
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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V
R1
R2
Qi
Ti
Qo
To
H
P
H sensor
Tsenso
r
Water heater (Physical process)
Dynamic Bayesian Network
Dynamic Bayesian Network


Factorized MC model
Factorized MC model
Application Water heater Reliability
WEBER P., JOUFFE L.,ComplexsystemreliabilitymodellingwithDynamicObjectOrientedBayesianNetworks (DOOBN). ReliabilityEngineering andSystem
Safety, Volume 91, Issue 2, February 2006, Pages 149162 (Selected Papers Presented at QUALITA 2003).
MULLER A., WEBER P., BEN SALEM A.Process modelbased Dynamic Bayesian Networks for Prognostic. IEEE 4th International Conference on Intelligent
Systems Design and Applications (ISDA 2004), Budapest, Hungary, August 2628, 2004.
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Water heater (Process model)
To regulate the
input water flow
rate
Valve
Input Water Flow
To heat water
Heating
resistors
To measure the
water temperature
Temperature
sensor
To measure the
water level
Level sensor
To distribute water
Water pipe
To control the
'Water heater'
process
PLC
Water level report
Water temperature report
Water distributed
& heated
To store water
Tank
Water to heatWater to heat
Water to distributeWater to distribute
Position order
Water to distribute (k)
Water distributed
& heated (k)
Heatin
g
order
E.E.
E.E.
E.E.
E.E.
E.E. = Electrical Energy
Dynamic Bayesian Network
Dynamic Bayesian Network


Factorized MC model
Factorized MC model
Application 2 Water heater Reliability
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
34
0.0
0.2
0.4
0.6
0.8
1.0
0
500100015002000
P(state1
)
P(state 2)
P(state 3)
P(state 4)
HEATING RESISTOR (k)
1
2
λ
1
4
λ
2
3
λ
4
λ3
λ
5
R1
R1
and
and
R2 max
R2 max
R1 or R2 down
R1 or R2 down
Action:
Action:
to repair the
to repair the
heating resistor
heating resistor
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Water heater (Probabilistic model DBN)
1
2
λ
1
4
λ
2
3
λ
4
λ
3
λ
5
Dynamic Bayesian Network
Dynamic Bayesian Network


Factorized MC model
Factorized MC model
Application 2 Water heater Reliability
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
36
To provide
Warm Water
HD1
Order T=50°C
AD2 water input
pressure and Ti
AD4
WATER HEATER PROCESS
RHD water output
temperature T
and flow rate Qo
AD1 Electric
Power
AD3 system
parameters
temperature T
and level H
To transform
Pressure
to Qi
HD Order V
A
D2 water input
pressure and Ti
A
D41
VALVE V
RHD Qi
A
D1 Electric
Power
AD
Ti
To transform
H to Qo
A
D44
WATER PIPE
RHD water output
flow rate Qo
HD1
Order T=50°C
To transform
Qi to H
Ti to T
AD
Qi
A
D43
TANK, HEATING RESISTOR
RHD water output
temperature T
AD1 Electric
Power
To control
V and P
A
D42 COMPUTER,
SENSORS
HD Order P
A
D3 system
parameters
temperature T
and level H
A
D1 Electric
Power
AD water
level H
RHD V
RHD P
A1
A2
A3
A4
RHD water
level H
Water heater (SADT model and OODBN model)
Dynamic Bayesian Network
Dynamic Bayesian Network


Factorized MC model
Factorized MC model
Application 2 Water heater Reliability
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
37
AD Ti
T
o hea
t
water
from Ti to T
AD Qi
A
D43
HEATING RESISTOR
RHD water
temperature T
AD1 Electric Power
HD Order P
A3
AD43
TANK
To stock
water
Qi to H
RHD water level H
A31
A32
AD water
level H
to heat water
to stock water
AD Ti
AD Qi
RHD level H
RHD temperature T
AD Electric Power
HD Order P
EF to stock water
AD Qi
TANK
RHD level H
EF to heat water
AD Ti
HEATING RESISTOR
A
D Electric Power
HD Order P
AD water level H
RHD temperature T
Application 2 Water heater
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
38
EF to heat wate
r
AD Ti
HEATING RESISTOR
AD Electric Power
HD Order P
AD water level H
RHD temperature T
EF to stock water
AD Qi
TANK
RHD level H
RHD waterlevelH
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
400
800
1200
1600
2000
P(correct)
P(incorrect)
EF to heatwater(k)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
500
100015002000
P(state1)
P(state2)
P(state3)
P(state4)
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
39
RHD water output temperature T(k)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
500 1000 1500 2000
P(correct)
P(incorrect)
RHD water output flow rate Qo (k)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
400
800120016002000
P(correct)
P(incorrect)
To transform
Pressure
to Qi
HD Order V
AD2 water input
pressure and Ti
A
D41
VALVE V
RHD Qi
A
D1 Electric
Power
AD
Ti
To transform
H to Qo
A
D44
WATER PIPE
RHD water output
flow rate Qo
HD1
Order T=50°C
To transform
Qi to H
Ti to T
AD
Qi
A
D43
TANK, HEATING RESISTOR
RHD water output
temperature T
A
D1 Electric
Power
To control
V and P
A
D42 COMPUTER,
SENSORS
HD Order P
AD3 system
parameters
temperature T
and level H
AD1 Electric
Power
AD water
level H
RHD V
RHD P
A1
A2
A3
A4
RHD water
level H
Application 2
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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A safety barriersbased approach for the risk
analysis of sociotechnical systems
LEGER A., DUVAL C., WEBER P., LEVRAT E., FARRET R.,Bayesian Network Modellingthe risk
analysis of complex socio technical systems. Workshop on Advanced Control and Diagnosis, ACD'2006,
Nancy, France (16/11/2006).
DUVAL C., LEGER A., WEBER P., LEVRAT E., IUNG B., FARRET R.,Choice of a risk analysis method
for complex sociotechnical systems. European Safety and Reliability Conference, ESREL 2007,
Stavanger, Norvège(25/06/2007).
Application Risk analysis of sociotechnical systems
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A global risk analysis model
A global risk analysis model
Ein 1
Ein 2
Ein 3
Ein 4
Ein 5
Ec 6
Ein 7
Ec 8
EI
EI
EI
EI
EI
EI
ERC
ERS
ERS
PhD
PhD
PhD
PhD
EM
EM
EM
EM
EM
EM
&
Or
&
Or
Or
Or
Or
Decision a
Decision b
Organisational
factor a
Organis
ational
factor
b
Internal organisational layer
Decisions and actions layer
Technical layer
External organi
s
ational
layer
N
atural environment laye
r
Organisational
factor
c
Organisational
factor
d
Environmental
factor
a
Environmental
factor b
Transactional exchange
Vertical exchange
Horizontal exchange
Caption
Risk reduction barrier
PatéCornell M.E.Murphy D.M.,‘Humanand management factors in probabilistic risk analysis: the SAM approach and
observations from recent applications’, Reliability Engineering and System Safety, n°53, pp. 115126, 1996.
Necessity to establish relations between different kinds of layersin the
model of the system: the technical layer (closed system)andthe
human/organisational layer (open system)
Application Risk analysis of sociotechnical systems
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
42
A global risk analysis model
A global risk analysis model
The generic global Bayesian network model structure
The generic global Bayesian network model structure
Internal
Internal
organisational
organisational
layer
layer
Application Risk analysis of sociotechnical systems
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
43
Application Risk analysis of sociotechnical systems
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
45
Conclusion
Bayesian Networks
–Equivalence between the Bayesian Networks and fault tree…
–Multimodal model
–Acyclic Graph constraint only
Dynamic Bayesian Networks
–Equivalence between the Dynamic Bayesian Networks and MC,
½MC, MSM, IOHMM
–
–
Thanks to the factorization,
Thanks to the factorization,DBN leads to a synthetic
representation of complex systems
Actual works
Actual works
–PRM application in Maintenance SKOOB ANR project
–Evidential Networks in reliability
SIMON C., WEBER P., Bayesian Networks Implementation of the DempsterShafer Theory to Model Reliability Uncertainty. Workshop on Bayesian
Networks in Dependability (BND2006) in the First International Conference on Availiability, Reliability and Security, ARES 2006, Vienna, April 2022,
Autriche(2006), pp. 788793, (2006).
Club Automation 30sep 2010, CRAN UMR 7039 CNRS, Nancy Université
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Someref.
WEBER P., JOUFFE L., ComplexsystemreliabilitymodellingwithDynamicObjectOrientedBayesianNetworks (DOOBN). ReliabilityEngineering and
SystemSafety, Volume 91, Issue 2, pages 149162 (Selected Papers Presented at QUALITA 2003) February (2006).
WEBER P., SUHNER M.C., IUNG B. System approachbased Bayesian Network to aid maintenance of manufacturing process. 6th IFAC Symposium on
Cost Oriented Automation, Low Cost Automation, Berlin, 89 octobre, (2001).
WEBER P., SUHNER M.C. An application of Bayesian Networks to thePerformance Analysis of a Process. European Conference on System Dependability
and Safety (ESRA 2002/lambdaMu13), Lyon (France), 1921 mars (2002).
WEBER P., JOUFFE L. Reliability modelling with Dynamic Bayesian Networks. 5th IFAC Symposium on Fault Detection, Supervision andSafety of
Technical Processes (SAFEPROCESS'03), Washington, D.C., USA, 911 juin, (2003).
WEBER P., MUNTEANU P., JOUFFE L. Dynamic Bayesian Networks modelling the dependability of systems with degradations and exogenous constraints.
11th IFAC Symposium on Information Control Problems in Manufacturing, INCOM'04. SalvadorBahia, Brazil, April 57th, (2004).
MULLER A., WEBER P., BEN SALEM A. Process modelbased Dynamic Bayesian Networks for Prognostic. Fourth International Conference on Intelligent
Systems Design and Applications (ISDA 2004), Budapest, Hungary, August 2628, (2004).
BOUILLAUT L., WEBER P., BEN SALEM A., AKNIN P. Use of Causal Probabilistic Networks for the improvement of the Maintenance of Railway
Infrastructure. IEEE International Conference on Systems, Man and Cybernetics, Hague, Netherlands, October 1013, (2004).
BEN SALEM A., BOUILLAUT L., AKNIN P., WEBER P. Dynamic Bayesian Networks for classification of rail defects. IEEE 4th International Conference
on Intelligent Systems Design and Applications, Budapest, Hungary, August 2628, (2004).
BEN SALEM A., MULLER A., WEBER P., Dynamic Bayesian Networks in system reliability analysis. 6th IFAC Symposium on Fault Detection,
Supervision and Safety of Technical Processes, Beijing, P.R. China (30/08/2006), pp. 481486, (2006).
WEBER P., THEILLIOL D., AUBRUN C., EVSUKOFF A.G., Increasing effectiveness of modelbased fault diagnosis: A Dynamic Bayesian Network
design for decision making. 6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Beijing, P.R. China
(30/08/2006), pp. 109114, (2006).
SIMON C., WEBER P., Bayesian Networks Implementation of the DempsterShafer Theory to Model Reliability Uncertainty. Workshop on Bayesian
Networks in Dependability (BND2006) in the First International Conference on Availiability, Reliability and Security, ARES 2006, Vienna, April 20
22, Autriche(2006), pp. 788793, (2006).
LEGER A., DUVAL C., WEBER P., LEVRAT E., FARRET R., Bayesian Network Modellingthe risk analysis of complex socio technical systems.
Workshop on Advanced Control and Diagnosis, ACD'2006, Nancy, France (16/11/2006).
DUVAL C., LEGER A., WEBER P., LEVRAT E., IUNG B., FARRET R., Choice of a risk analysis method for complex sociotechnical systems. European
Safety and Reliability Conference, ESREL 2007, Stavanger, Norvège(25/06/2007).
References of CRAN are available with HAL
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