1. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 1 Assigning Tolerances to J-Values used in Safety Analysis James Kearns (2 nd Year PhD Student) Supervisor: Professor Philip Thomas School of Engineering and Mathematical Sciences City University, London EC1V 0HB

2. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 2 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.

3. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 3 The J-Value & Input Parameters ε: Coefficient of Risk Aversion δV N : Cost of protection system (£) N: Population affected by hazard G: GDP per person per year (£/y) δX d : Change in life expectancy (y)

4. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 4 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

5. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 5 J-Value Analysis: AP1000 Rejected Safety Systems

6. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 6 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.

7. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 7 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).

8. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 8 Population Distributions

9. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 9 Work-Time Fraction Distributions

10. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 10 Uncertainty Propagations ~20 Input Parameters which contribute to the J-Value uncertainty. J δV N δX d NGε Case-DependentCase-Independent n Pop w0w0 θ GDP Xy p(a) MICOE p w (a) g w (a)S(a) n sv TsTs

11. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 11 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.

12. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 12 Results: Risk Aversion

13. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 13 Results: J-Value Test case with J = 1 for both actual distributions. σ G = 0.75%. Here assumed σ δX = σ δV = σ N =0. Variances: 2 % for all.

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

15. Universities Nuclear Technology Forum, April 14-16, 2010, Salford 15 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 6  11, 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