Who Cares About Uncertainty in Risk Models? Just More Number Crunching?

CRA PSA/HFA 5th Annual Forum 2014 Ashraf El-Shanawany

CONTENTS

■ PART I: WHY BOTHER WITH UNCERTAINTY IN RISK MODELS?

■ PART II: HOW TO INCORPORATE UNCERTAINTY

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PART I: WHY BOTHER WITH UNCERTAINTY IN RISK MODELS?

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■ Conservatism is ubiquitous in engineering calculations ■ Serves a valuable practical purpose

■ Provides a way of implicitly allowing

for approximated uncertainties

Conservatism

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Conservatism Serves A Useful Purpose

BUT …

■ Conservatism distorts risk results

■ A simple example maintenance & time at risk problem will be used as illustration

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Time at Risk

Maintenance & Time At Risk

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System X has two protective barriers, A & B. Each has a pfd of: • Conservative 1E-02 • Best estimate 1E-03

Maintenance & Time At Risk

■ Even in this simplest case the conservative estimate

underestimates the proportion of risk incurred during maintenance states

■ Consider two cases for the plant risk over the course of a year

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Maintenance & Time At Risk

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Percentage Contribution of Maintenance

Proportion of time in Maintenance State

Conservative Best Estimate

Case 1: pM = 12 hours per 365 days

12% 58%

Case 2: pM = 4 days per 365 days

53% 92%

But Why Uncertainty? …

■ An argument for best estimates over conservative

estimates has been presented

■ But, conservative estimates implicitly allow for (one-sided) uncertainty

■ This allowance is lost if a single best estimate value is used

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Best Estimates

■ Best estimates are vulnerable to high uncertainty ■ An accurate best estimate may still be a poor description

of the failure parameter

■ An estimate of the uncertainty allows the direct use of best estimates

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Best Estimates In Context of Uncertainty

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Why Uncertainty?

The explicit inclusion of uncertainty:

Retains the benefits of using a best estimate over a

conservative estimate Provides an allowance for parameters with a high

coefficient of variation

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Conservatism Is Compounded By PSA Models

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Conservatism is compounded throughout a PSA model: so the effect gets stronger in real models

When To Include Uncertainty

Conservatism is a powerful simplifying tool

The main value of probabilistic models is comparing and balancing risks Conservatism can significantly distort these relative risks

Where (economically) possible conservatism should

be replaced by best estimate plus uncertainty

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PART II: HOW TO INCORPORATE UNCERTAINTY

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+ξ

Where’s the uncertainty?

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Heat Generation &

Removal

Temperature Measurements

Model of Temperature

Variation

Thermo-hydraulic Code

Plant Heat Exchange

Requirements Risk Model

Risk Informed Decisions

+ξ

+ξ +ξ

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Physical Processes

Observations

Theoretical Model

Numerical Solutions

Plant Success Criteria

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What Types of Uncertainty Are There?

Uncertainty is typically classified into: “Statistical (aleatory) uncertainty”

“Epistemic uncertainty”

Most uncertainties have elements of both

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Some Sources of Uncertainty in Risk Models

■ Plant Equipment Failure Parameters (A) ■ Hazard Frequencies (A)

Internal & External ■ Quantification of CCFs (A/E) ■ Success Criteria (E) ■ Human Factors (A) ■ Assumptions (E) ■ Bounding Analyses (E) ■ Model Completeness (A/E)

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Uncertainty in Success Criteria Example

Success criteria define the PSA model structure

Success criteria uncertainty has the potential to significantly impact the model

(Part of) the success criteria for shutdown of a nuclear reactor is considered The Xenon-135 transient post-trip affects reactivity

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Xenon and Neutrons

Xenon-135 is a fission product and a strong neutron absorber

Post trip it will build up and then decay

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Xenon Transient Post Trip

When the Xe-135 concentration falls below the concentration at the time of trip there is an effective reactivity insertion

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Xenon Transient Post Trip

The effect of Xe-135 decay may be important for long term reactivity management in some scenarios

N2 can be used to provide hold-down margin for the reactor in these scenarios

The time within which N2 is needed depends on the Xe-135 transient

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Xenon Transient Post Trip

The Xe-135 transient depends primarily on the reactor power pre-trip

The reactor power is variable

A conservative estimate would normally be used for the time requirement for nitrogen injection

What happens if the conservative estimate is replaced with a best estimate plus uncertainty?

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Example Fault Tree Analysis

A simple test case fault tree model has been setup to evaluate the affect of time uncertainty

The fault tree models a hypothetical plant for providing nitrogen gas

A single operator action is included in the fault tree model

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Example Fault Tree

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Simplified Example Fault Tree

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Base Case and Uncertain Case

BASE CASE: HEP is evaluated based on a conservative time available for completion of the action

UNCERTAINTY CASE: HEP is evaluated as a distribution based on the distribution of the expected amount of time available for completion of the action Plus an intuitive model of the effect of time on reliability

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Comparison Results Table

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ID Sequence Probability

Percentage Contribution

Event 1 Event 2

1 1.00E-03 49.8 OP2 2 9.00E-04 44.8 PB1 3 1.00E-04

4 1.00E-05

5 1.00E-06 0.05 PB3 PB4

ID Sequence Probability

Percentage Contribution

Event 1 Event 2

1 9.00E-04 62.1 PB1 2 4.38E-04 30.2 OP1 3 1.00E-04

4 1.00E-05

5 1.00E-06 0.07 PB3 PB4

Conservative Case

Uncertainty Case

The Effect on the Risk Predictions

The ordering of the cutsets is changed

The importance rankings of basic events are changed

Of less significance: the predicted probability of failure on demand is changed slightly

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Conclusions

The move from conservatism to best estimate plus uncertainty can have a significant effect on the risk profile

Uncertainty can arise from numerous different analysis domains, and in general can be usefully propagated into PSA models

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Conclusions

Success criteria uncertainty is a ubiquitous source of uncertainty that is minimally handled in current PSA models

The iterative inclusion of sources of success criteria

uncertainty has the potential to significantly alter estimated risk profiles

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Conclusions

The inclusion of uncertainty needs to be balanced against practical considerations

The order in which uncertainties should be incorporated into PSA/PRA models is not yet clear

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Final Thought

For the avoidance of doubt, consider everything to be uncertain

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