Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Assigning Tolerances to J-Values used in Safety Analysis

James Kearns(2nd Year PhD Student)

Supervisor: Professor Philip ThomasSchool of Engineering and Mathematical Sciences

City University, London EC1V 0HB

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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The J-Value Method

• An objective method of assessing appropriate levels of expenditure on safety systems.

• Ensures consistency when making decisions which affect human life.

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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The J-Value & Input Parameters

• ε: Coefficient of Risk Aversion

• δVN: Cost of protection system (£)

• N: Population affected by hazard• G: GDP per person per year (£/y)

• δXd: Change in life expectancy (y)

d

N

XNG

VJ

ˆ1

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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• If J > 1:

- The safety scheme is too expensive.

• If J < 1:

- The safety scheme represents good value for money.

• J = 1 represents the maximum reasonable cost.

The J-Value & Input Parameters

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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J-Value Analysis: AP1000 Rejected Safety Systems

1

10

100

1,000

10,000

100,000

J-Value, 0%Discount Rate

J-Value, 2.5%Discount Rate

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Assigning Tolerances and Investigating Sensitivities

• Recent work has focused on obtaining accurate evaluations of J-value input parameters and their tolerances.

• Sensitivity analyses have also been performed to test assumptions of the J-Value model.

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Assigning Tolerances and Investigating Sensitivities

• The assumptions tested for sensitivity were: – Population distribution

(steady state vs actual observed).– Work-time fraction distribution

(rectangular vs actual observed).– Variation over time

(parameters projected to 2080).

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Population Distributions

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 20 40 60 80 100 120

Age

p(a) steady state

p(a) actual

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Work-Time Fraction Distributions

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 20 40 60 80 100 120

Age

v(a) rectangular

v(a) actual

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Uncertainty Propagations• ~20 Input Parameters which contribute to the J-Value uncertainty.

J

δVNδXdNG ε

Case-DependentCase-Independent

nPop w0 θ

GDPXy

GDP

p(a)

MICOE

pw(a)gw(a) S(a)

nsv Ts

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Results: Risk Aversion

•Variances: 0.4% (all).•Changing from actual p(a) to steady state increases ε by 0.001.•Changing v(a) from actual to rectangular increases ε by 0.001 – more risk averse.

Risk Aversion, ε

0.81

0.815

0.82

0.825

0.83

0.835

ε+σε 0.8253702 0.8265389 0.8263743 0.8275432

ε-σε 0.8186298 0.8194611 0.8196257 0.8204568

ε 0.822 0.823 0.823 0.824

p(a) act, v(a) act p(a) act, v(a) rec p(a) steady, v(a) act p(a) steady v(a) rec

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Results: Risk Aversion

0.82

0.825

0.83

0.835

0.84

0.845

0.85

0 10 20 30 40 50 60 70 80 90

act & actact & steady

act & recsteady & rec

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Results: J-Value

• Test case with J = 1 for both actual distributions. σG = 0.75%.

• Here assumed σδX = σδV= σN=0.

• Variances: 2 % for all.

J Value

0.920

0.940

0.960

0.980

1.000

1.020

1.040

J+σJ 1.022 1.016 1.016 1.010

J-σJ 0.978 0.973 0.973 0.967

J 1.000 0.994 0.994 0.989

p(a) act, v(a) act p(a) act, v(a) rec p(a) steady, v(a) act p(a) steady v(a) rec

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Summary

• “Internal Accuracy” of J-value is within 2%• J-value model is very insensitive to initial

assumptions.• Simplified assumptions reduce uncertainties,

give slightly more conservative J-values, and reduces the complexity of the J-value model.

• This justifies the use of such assumptions.• Slow time variation.

Universities Nuclear Technology Forum,April 14-16, 2010, Salford

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Thank You!

• Further Information:– Thomas, P., Jones, R. and Kearns, J., 2010, “The Trade-Offs Embodied in

J-Value Safety Analysis”, Process Safety and Environmental Protection, in press, doi: 10.1016/j.psep.2010.02.001

– Thomas, P., Jones, R. and Kearns, J., 2009, "Measurement of parameters to value human life extension", XIX IMEKO World Congress, Fundamental and Applied Metrology, September 611, 2009, Lisbon, Portugal

– Thomas, P. and Stupples, D., 2007, "J-value: a new scale for judging health and safety spend in the nuclear and other industries", Nuclear Future ,Vol. 03, No. 3, May/June