Risk & Uncertainty - CentraleSupelecli/materials/lecture_Enrico_risk_uncertainty.pdf · The (The (uncertain uncertain) flow of the ) flow of the presentationpresentation PARTI I:

Risk & UncertaintyRisk & Uncertainty

Enrico Zio

The (The (uncertainuncertain) flow of the ) flow of the presentationpresentation

PARTI I: The uncertainty of risk

� Problem Setting: RISK, QRA, PRA

� Uncertainty: types and sources

� Worries

� Frameworks of uncertainty/information/knowledge representation

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Introduction to exploration activities 2Agip KCO

Piping and long distance pipelines2

PART II: The risk of uncertainty

� Decision maker dreams and nightmares

The (The (riskyrisky) flow of the ) flow of the presentationpresentation

PART III: “Things I know”

� “Faithful” representation of information and introduction of knowledge

PART IV: Jingles

� Conclusions

� Advertisement

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� Advertisement

� Thanks

PART I: The uncertainty of risk

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Safety

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Piping and long distance pipelines

Hazard

barrier

The parmesan The parmesan cheesecheese modelmodel

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No Hazard

No

Redundancy Training Safety Reviews

Multiple Multiple barriersbarriers

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No Hazard

Hazard

RedundancyRedundancy exampleexample

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Geological Barrier

Technical BarriersEmbeddingStorage caskOver packsBackfill

Multiple Multiple barrierbarrier system system exampleexample

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Waste

Coated particle

Inner graphite zone

Fuel-free graphite zone

60 mm

0.5 mm

0.095 mm0.040 mm

0.035 mm0.040 mm

PyC PyCSiC buffer fuel

Multiple Multiple barrierbarrier system system exampleexample

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Graphite matrix Outer PyC SiC Inner PyC Kernel

Risk

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Not all risk mitigation strategies work...

Reality: an Reality: an exampleexample of a protection of a protection barrierbarrier

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Hazard

HumanErrors

ProceduralErrorsFaults in

Redundancies

The The swissswiss cheesecheese modelmodel

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Hazard

Safeguards

Environment

UNCERTAINTY

The concept of RiskThe concept of Risk

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People

UNCERTAINTY

1. What undesired conditions may occur? ? Accident, A

3. What is the likelihood (uncertainty) of occurren ce? Uncertainty, L( U)

Risk = (A, C, U)

Risk and Quantitative Risk Risk and Quantitative Risk AnalysisAnalysis (QRA)(QRA)

2. What damage do they cause? Consequence, C

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3. What is the likelihood (uncertainty) of occurren ce? Uncertainty, L( U)

Quantitative Risk Analysis Model =(a, c, l(u), K)

Alternative 1 Alternative 2

- Design configuration 1- Redundancy allocation 1- Evacuation plan 1

- Design configuration 2- Redundancy allocation 2- Evacuation plan 2

Risk and Quantitative Risk Risk and Quantitative Risk AnalysisAnalysis (QRA)(QRA)

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RISK 1 RISK 2

C: How many fatalities C1?

L: What is the likelihood of having C1 fatalities or more?

C: How many fatalities C2?

L: What is the likelihood of having C2 fatalities or more?

A

SYSTEMRISK

MODEL“ λ is between 10 -3 and 10 -2 [h -1]”

KN

OW

LED

GE

K

(UNCERTAIN)

Quantitative Risk Quantitative Risk AnalysisAnalysis

tX

tX

…

valve 1

valve 2

valve N

…

t1

t2

tNtX

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“ λ is between 10 and 10 [h ]”

“ λ is quite small”

KN

OW

LED

GE

K

REPRESENTATIONOF UNCERTAINTY

MUNCERTAINTYPROPAGATION

(UNCERTAIN)RISK MEASURES

(a,c,u,M,K)

SYSTEMRISK

MODEL

…0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

1

2

3

4

5

6

7

8

9

probability density function

Er

t

“ λ is UNIFORM

KN

OW

LED

GE

K

valve 1

valve 2

valve N

fT(t, λ)

(PROBABILISTIC)

Probabilistic Risk AnalysisProbabilistic Risk Analysis

fz (Z)

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“ λ is UNIFORMbetween 10 -3 and 10 -2 [h -1]”

“ λ is less than 10 -2 [h -1] with probability 0.9”

KN

OW

LED

GE

K

PROBABILISTICREPRESENTATIONOF UNCERTAINTY

(M=P)

UNCERTAINTYPROPAGATION

(PROBABILISTIC)RISK MEASURES

(a,c,u,P,K)

Uncertainty

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Uncertainty is not in the things but in our head: uncertainty is lack of knowledge

J. Bernoulli

20

Imprecise character of measurement or

conclusion

Imprecise or vague character of picture perception

Unforeseen character of results issued from action

or evolution

Uncertainty

Characteristic of who is uncertain

Being of someone who does not know what to decide

Uncertainty (in the dictionary)Uncertainty (in the dictionary)

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or evolution

Impossibility for person to foresee or to know in

advance his behavior or events by which he will be

concerned

[TLFi : Trésor de la Langue Française Informatisé]

Perturbing state of person waiting for the uncertain

events

Accent on the subjectAccent on the object

Adapted from S. Farnoud and S. Tillement, IFIS Toulouse 2010

21

Uncertainty

From latin certus

from latin certitudo

Uncertainty (in the epistemology)Uncertainty (in the epistemology)

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From the latin verb cernere

« discern, decide »

from latin cerno : from common indo-european (s)ker :

cutcut, which pairs it with the ancient greek krino : shear


22 Modern era airmoderne

– Socrate, Platon, Carnéade

– Sophism

Renaissance

Middle Ages

2000

500

1500

Incoherence of philosophies of Ghazali, necessity to prove the validity of reason, independent from

reason.

Descartes, Pascal, Kant

Laplace, Carnap, Shackle, Gödel

De Finetti, Knight, Zadeh, …

Uncertainty (in the history)Uncertainty (in the history)

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Prehistory

– The development of Homo sapiens in an uncertain environment: predator, war ....

Chimpanzees still live in this environment [Philippe De Wilde 2010].

– Evolution has selected the anatomy of the brain that is optimized to some degree to

cope with uncertainty[Philippe De Wilde 2010].

– Sophism

– Skepticism

– 500 before J.C. Empédocle d'Agrigente (father of rhetoric), Gorgias

– Mathematics were used to create confidence [Philippe De Wilde 2010].

– Logic provides reasoning rules to reduce uncertainty.

– Religion provides a narrative to create confidence [Philippe De Wilde 2010].

– Mythe was the first attempt to reduce uncertainty [Gérald Bronner 1997].

-1000

0

- 500

Antiquity

-3000


UncertaintyUncertainty in QRAin QRA

» reducible uncertainty» property of the analyst» lack of knowledge or

aleatory uncertainty

» irreducible uncertainty» property of the system» random

epistemic uncertainty

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Adapted from G. Apostolakis, Workshop LA 2010 and M. Beer, Seminar Paris 2012

» lack of knowledge or perception» random

fluctuations / variability/ stochasticity


» reducible uncertainty» property of the analyst» lack of knowledge or

aleatory uncertainty

» irreducible uncertainty» property of the system» random

epistemic uncertainty

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Adapted from G. Apostolakis, Workshop LA 2010 and M. Beer, Seminar Paris 2012

» lack of knowledge or perception» random

fluctuations / variability/ stochasticity

�Epistemic uncertainties are further categorized as being due to parameter values, modelassumptions, and incomplete analyses (“Known unknowns” – initiating events, failure modes or mechanisms are known but not included in the model; “Unknown unknowns” – phenomena or failure mechanisms are unknown)


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failure mechanisms are unknown)

Adapted from G. Apostolakis, Workshop LA 2010

p1

p

{S1, lS1, c1}

{S2, lS2, c2}

{S3, lS3, c3}

{S4, lS4, c4}

1 ‒ p1

1 – p2

p2

1 – p2ALEATORYALEATORY

Initiator Event (IE)

Event 1: Shut-down valve

Event 2: Emergency andevacuation procedure

(aleatory and epistemic) Uncertainty in QRA(aleatory and epistemic) Uncertainty in QRA

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p2{S4, lS4, c4}

EPISTEMICEPISTEMIC

Aleatory : variability , randomness (in occurrence of the events in thescenarios)Epistemic : lack of knowledge/information ( on the values of the parameters of the probability and consequence models)

p1

p

{S1, lS1, c1}

{S2, lS2, c2}

{S3, lS3, c3}

{S4, lS4, c4}

1 ‒ p1

1 – p2

p2

1 – p2ALEATORYALEATORY

Initiator Event (IE)

Event 1: Shut-down valve

Event 2: Emergency andevacuation procedure

((aleatoryaleatory and and epistemicepistemic) ) UncertaintyUncertainty in PRAin PRA

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p2{S4, lS4, c4}

EPISTEMICEPISTEMIC

Aleatory : STOCHASTIC MODELS

Epistemic : PROBABILITIES

Probability used for representing both randomness and incomplete

information/partial knowledge

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Sufficiently informative (statistical) data : P=limiting relative frequency (chance); in practice, estimated value P*

tX

tX

tX

…

valve 1

valve 2

valve N

…

t1

t2

tN

Hardware failure occurrence times: Event 1 = failure of shut-down valve

Probablistic representation of Probablistic representation of epistemic uncertainty in PRAepistemic uncertainty in PRA

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Realizations of a random variable � Probability Density Function

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

1

2

3

4

5

6

7

8

9

probability density function

E

t

f*T(t, λ*)

P(A/K)

�Betting interpretation:

� The probability of the event A, P(A), equals the amount of money that the assigner would be willing to bet if he/she would receive a single unit of payment in the case that the

event A were to occur, and nothing otherwise.

Probablistic representation of Probablistic representation of epistemic uncertainty in PRAepistemic uncertainty in PRA

Scarce (possibly qualitative) data : P(A/K)=Subjective probability (knowledge-based probability)

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event A were to occur, and nothing otherwise.

�Comparison with a standard

� The assessor compares his/her uncertainty about the occurrence of the event A with e.g. drawing a favourable ball from an urn that contains P(A) · 100 % favourable

balls (Lindley, 2000).

Adapted from T. Aven, Workshop LA 2010

PRA

EpistemicEpistemic UncertaintyUncertainty

lK = (Statistical) Data

M = Frequentist Probability

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PRA

30

K = Beliefs

M = Subjective Probability

c

Worries

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In risk analysis assumptions are made that may be convenient but not really justified from the available information and knowledge:

� Distributions are stationary (unchanging in time)

� Variables, experts are independent of one another

� Uniform distributions model “complete” uncertainty

Worries: known unknownsWorries: known unknowns

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� Uniform distributions model “complete” uncertainty

Adapted from S. Ferson, Workshop LA 2010

Uniform Uniform Uniform Uniform


Instability

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Prob

abil

ityde

nsit

y


UniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniformUniform

The more (uncertain)

Prob

abil

ity d

ensi

ty


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inputs, the more certainty in the output: Where does this surety/confidence come from?What justifies it?

Prob

abil

ity d

ensi

ty


Worries: unknown unknownsWorries: unknown unknowns

Elicited probabilities are impreciseuncertainties ”hidden” in K

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P(health problems | K) =0.01

SurprisesAdapted from T. Aven, Workshop LA 2010

Frameworks of uncertainty/information/knowledge

representation

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Uncertainty representationUncertainty representation

Tools for representing uncertainty

– Probability distributions : good for expressing

variability, but information-demanding and thus becomes paradoxical when information is incomplete (choice of a

single distribution not satisfactory)

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Adapted from D. Dubois, Workshop LA 2010

– Sets (numerical intervals): good for representing

incomplete information, but a very crude representation of uncertainty

Find representations that allow for both aspects ofuncertainty


Representations that allow for both aspects of uncertainty

� Frameworks capable of distinguishing between uncertainty due to variability from uncertainty due to lack of knowledge or

missing information� More informative than the sets of pure interval (or classical)

logic

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logic� Less demanding than single probability distributions� Explicitly allowing for missing information

Blend intervals and probability


Blending intervals and probability

� Sets of probabilities: imprecise probability theory ([P*(A), P*(A)])

� Random sets: Dempster-Shafer Theory ([Bel(A),Pl(A)])

� Fuzzy sets: numerical possibility theory ([Π(A,N(A)])

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Instead of a single degree of probability, each event A has a degree of belief (certainty) and a

degree of plausibility which “bound all probabilities”


Practical ways for representing probability sets

• Fuzzy (numerical) intervals (possibility theory)• Probability intervals (bounding the probabilities of

events)• Probability boxes (pairs of pdfs or cdfs)

• Generalized p-boxes (pairs of co-monotonic possibility

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• Generalized p-boxes (pairs of co-monotonic possibility distributions)

• Clouds (pairs of possibility distributions)

(Some are special random sets, others not)

Example: P-box

1

Interval bounds on a cdf


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01.0 2.0 3.00.0 X

cdf


Probability Bounds Framework: what it does

�Bridges qualitative information and quantitative data

�Distinguishes variability and incomplete knowledge

�When data are abundant, it is equivalent to probability theory

�When data are sparse, it yields both conservative and optimistic results


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optimistic results

� It enables representing the continuum of situations between these extremes

�Accounts for uncertainties of both kinds about

�Parameters

�Distribution shapes

�Dependencies among variables

�Structure of the model





Bounded Probability Risk Analysis

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M = Imprecise ProbabilityRandom Sets (D-S Theory)Possibility theory

K = Beliefs

c

PART II: The risk of uncertainty

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Decision maker dreams…Decision maker dreams…

Probability Bounds: how to use the results

�When uncertainty makes no difference

bounding gives confidence in the reliability of the decision

Offshore

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cdf

Offshore plant 2

Offshore plant 1

Probability Bounds: how to use the results

�When uncertainty swamps the decision

use results to identify issues to further investigate

…and nightmares…and nightmares

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cdf

Offshore plant 1

Offshore plant 2

Can uncertainty swamp the decision?

�Yes, if large

�Too wide bounds: need to get more information and knowledge in the analysis


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� If not possible … do not force unjustifiable behavior into the analysis

results should not mislead decisions


PART III: “Things I Know”

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THINGS

Things I know: InformationThings I know: Information--based boundsbased bounds

cdf

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Do not add knowledge that is not included in the available

information

cdf

ThingsThings I know: (expert) I know: (expert) knowledgeknowledge--basedbased boundsbounds

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Do add expert knowledge when reliable

cdf

ThingsThings I know: (expert) I know: (expert) knowledgeknowledge--basedbased boundsbounds

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Do add expert knowledge when reliable

PART IV: Jingles

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Concluding remarks

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Probability Bounds Framework

�Combines interval and probability methods, generalizing them: analyst can relax (towards interval analysis) or tighten (towards probability analysis) his/her assumptions, depending on what the information and knowledge on the problem justifies

Concluding remarksConcluding remarks

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information and knowledge on the problem justifies

�Allows distinguishing variability (modeled as randomness, by methods of probability theory) from imprecise information/knowledge (modeled as ignorance, by bounding methods such as interval analysis)


Theoretical issues

� Operational definitions (betting-like, standard comparison-like) of uncertainty representation, according to given behavioral rationality

�Dependence and independence (objective and epistemic) of information and (expert)


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epistemic) of information and (expert) knowledge sources

� Information and knowkedge fusion

�Mathematical operations for uncertainty calculus (e.g. Dempster rule of combination)


Practical issues

�Constructing bounding (imprecise) probabilities, from data (statistics with interval data) from experts (elicitation of upper/lower bounds for faithful representaton of incomplete information/knowledge)

�Uncertainty propagation (computational

ConcludingConcluding remarksremarks

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�Uncertainty propagation (computational challenges of blending Monte Carlo simulation with interval mathematics)

�Representation of results with meaningful summary measures

�Updating with additional evidence

�Accounting for dependeces in information sources, when fusing them


Updating…

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cum

ulat

ive

prob

abili

ty, F

P (

B1)

Basic Event B1 (Case B)

0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pos

sibi

lity

valu

e, πP

(B

2)


0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pos

sibi

lity

valu

e, πP

(B

3)


0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of Basic Event B4, P(B4)

Cum

ulat

ive

prob

abili

ty, F

P (

B4)


Upper CDF

Lower CDF

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pos

sibi

lity

valu

e, πP

(B

5)


0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of Basic Event B6, P(B

6)

Cum

ulat

ive

prob

abili

ty, F

P (

B6)


Epistemically-uncertain Basic Event (BE) probabilities

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0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140



0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1



0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1


6 6

P(B5)

Pos

sibi

lity

valu

e3 additional tests: 2 failures, 1 success

priorposterior

1

Dependences…

0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Cum

ulat

ive

prob

abili

ty, F

P (

B1)


0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Pos

sibi

lity

valu

e, πP

(B

2)


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pos

sibi

lity

valu

e, πP

(B

3)


0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Cum

ulat

ive

prob

abili

ty, F

P (

B4)


Upper CDFLower CDF

0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pos

sibi

lity

valu

e, πP

(B

5)


0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of Basic Event B6, P(B

6)

Cu

mu

lativ

e p

roba

bilit

y, F

P (

B6)


“ Epistemic” dependence between BE probabilities

Epistemically-uncertain Basic Event (BE) probabilities

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0 0.002 0.004 0.006 0.008 0.01 0.012 0.0140


0 0.002 0.004 0.006 0.008 0.01 0.012 0.014Probability of Basic Event B5, P(B5)

“ Objective” dependence between BEs

10-4

10-3

10-2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P(X)

Cum

ulat

ive

prob

abili

ty

10-4

10-3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P(X)

Cum

ulat

ive

prob

abili

ty


PERFECT STORMS

the killing in Norway on 22 July 2011, when a man placed a car-bomb outside the government

office and massacred a number of people on the island of Utøya

outside Oslo.

the eruption of the Icelandic volcano, which

paralyzed the air traffic over the Atlantic and western Europe

for a while in 2010

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the Fukushima Daiichi nuclear disaster in Japan in March 2011

the financial crisis that started in 2008

the failure of the BP DeepwaterHorizon platform

9/11 attacks on the US

…and …and nightmaresnightmares

BLACK SWANS



outside Oslo.



for a while in 2010

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9/11 attacks on the United States

The Decision Making process

� QRA results are one input to a subjective decision-making process

� Analytical results are debated and stakeholder values are included, within a deliberative process of decision-making

� Coherently with safety concepts such as defense-in-depth, multiple barriers and design basis accidents,


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depth, multiple barriers and design basis accidents, conservatism in the decisions is added where appropriate (to protect from the known and unknown unknowns)

Adapted from G. Apostolakis, Workshop LA 2010 and ANS DC 2012

Decision-Making ProcessUse a disciplined process to achieve the risk manag ement goal:

Identify issueIdentify Options

Analyze

DeliberateImplementDecision

Monitor

The one million euros question

€ € € € € €

“OK, these approaches are interesting, but does all of this actually make any practical difference in

real-world decisions?”

€ € € € € €


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(€ Are probability bounds/imprecise probabilities a more proper starting point than pure probability theory for robust and confident

decision making, faithful to information and knowledge?€)

(€ How to do it in practice? information before knowledge for faithfulness to information and unbiased exploitation of knowledge–bounds “as large as justified by information” + expert knowledge (without forcing) to see the effects in a “sensitivity analysis- like

process?€)

The one billion euros questionConcluding remarksConcluding remarks



Signals

Precursors

Near

PERFECT STORMS

€ € € € € € € € €

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c

M = ?

K = Beliefs

Signals Near misses

BLACK SWANS

Design Basis Accidents

Defense in depth




Signals

Precursors

Near

PERFECT STORMS

The one billion euros question

€ € € € € € € € €

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c

M = ?

K = Beliefs

Signals Near misses

BLACK SWANS

Design Basis Accidents

Defense in depth

Final Final remarksremarks

l

Precursors

Near

PERFECT STORMS

There are known knowns

But there are also unknownunknowns – the ones we don't

One should expect that the expectedcan be prevented, but theunexpected should have beenexpected

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c

SignalsNear

misses

BLACK SWANSWe also know there are knownunknowns; that is to say we knowthere are some things we do notknow.

unknowns – the ones we don'tknow we don't know.

Knowing ignorance is strength,ignoring knowledge is sickness

Knowing ignorance is strength, ignoring knowledge is sickness

Final Final remarksremarks

There are known knowns; there are things we know we know.We also know there are known unknowns; that is to say weknow there are some things we do not know. But there arealso unknown unknowns – the ones we don't know we don'tknow.

One should expect that the expected can be prevented, butthe unexpected should have been expected

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Knowing ignorance is strength, ignoring knowledge is sickness

PRA is a mature methodology, but there isstill quite some work to be done in order torender our systems safer.

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BACK UP SLIDESBACK UP SLIDES

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Lao Tsu, 600 BC

RISK MODEL (based on knowledge K)

Model inputVariables of interest

Measure of Uncertainty

Measure of uncertainty

Uncertainty propagation

Quantitative Risk AnalysisQuantitative Risk Analysis

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G(x)Model input

Xof interest

Z

UncertaintyM

uncertaintyM

Sensitivity analysis and importance ranking


�Model = representation of reality uncertainty

�Risk = (A,C,U)�Risk description=(A,C,U,M,K)

Quantitative Risk AnalysisQuantitative Risk Analysis

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�Risk description=(A,C,U,M,K)�Model error Z-G(X)≠0


�The mathematical theories for characterizing situations under uncertainty have been

�Set theory

�Probability Theory

�Since the mid 1960s, a number of generalizations of these classical theories became available for formalizing the various classical set theory and

Uncertainty in theoryUncertainty in theory

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72

formalizing the various classical set theory and probability theory

�The introduction of a number of alternative representations of uncertainty has sparked a lively discussion on their characteristics and usefulness

Adapted from G. Apostolakis, Workshop LA 2010

In practice: uncertainty and imprecision

separate treatment of uncertainty and imprecision

•

generalized models combining probabilistics and set theory

information defies a pure probabilistic modeling

» interval probabilities» p-boxes» random sets

Probability sets

••


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common basic feature:

set of plausible probabilistic models over a range of imprecision

» random sets» fuzzy random variables / fuzzy probabilities» evidence theory / Dempster-Shafer theory

bounds on probabilities for events of interest

(set of models which agree with the observations)

Adapted from M. Beer, Seminar Paris 2012

…and …and nightmaresnightmares



outside Oslo.



for a while in 2010

74Agip KCO






9/11 attacks on the United States

Documents

Risk & Uncertainty - CentraleSupelecli/materials/lecture_Enrico_risk_uncertainty.pdf · The (The (uncertain uncertain) flow of the ) flow of the presentationpresentation PARTI I: