Supporting papers
Latest publications
 Computing the Limits of Risk Aversion. (Waddington, I., Boyle, W. J. O., Kearns, J., 2013, Process Safety and Environmental Protection)
 Assigning tolerances to Jvalues used in safety analysis. (Kearns, J. O., Thomas, P. J., 2010, IMEKO TC1TC7 Joint Symposium)
 The limits to risk aversion. Part 2: The permission point and examples. (Thomas, P. J., Jones, R. D., Boyle, W. J. O., 2010, Process Safety and Environmental Protection)
These papers develop the Jvalue methodology of the core papers, presenting indepth analyses of the techniques and calculations required to use the Jvalue.

6. Thomas, P. J., Stupples, D. W., and Jones, R. D., 2007, "Analytical techniques for faster calculation of the life extension achieved by eliminating a prolonged radiation exposure", Trans IChemE, Part B, Process Safety and Environmental Protection, May, Vol. 85 (B3), 1 – 12.
The life extension achieved by a safety scheme that reduces or eliminates a prolonged radiation exposure is a necessary parameter for calculating the Judgmentor Jvalue, which enables the scheme's worth to be measured on a common, objective scale against which health and safety spend across all economic sectors can be assessed. The life expectancy calculation for radiation exposure is necessarily complex because of the long and stochastic incubation periods associated with radiationinduced cancers. Analytical methods are presented to reduce the size of this calculation approximately a hundredfold. This renders the Jvalue assessment much quicker and easier for new safety systems that may be considered for nuclear plant.

7. Jones, R. D., Thomas, P. J., and Stupples, D. W., 2007a, "Numerical techniques for speeding up the calculation of the life extension brought about by removing a prolonged radiation exposure", Process Safety and Environmental Protection, July, 85(B4), 269 – 276. Erratum: Process Safety and Environmental Protection, November, 85(B6), 599.
The judgement or Jvalue, which enables the worth of any health or safety scheme to be measured on a common, objective scale, may be applied to a scheme to reduce or eliminate a prolonged radiation exposure provided the life extension achieved can be calculated. The calculation is necessarily complex because of the long and stochastic incubation periods associated with radiationinduced cancers. However, numerical techniques are presented here that speed up the calculation of the improved life expectancy by a factor of about one hundred. The Jvalue assessment of new safety systems on nuclear plant is thus made much quicker and easier.

9. Jones, R. D., and Thomas, P. J., 2009, "Calculating the life extension achieved by reducing nuclear accident frequency", Trans IChemE, Part B, Process Safety and Environmental Protection, Vol. 87, 81 – 86.
Improvements in nuclear safety are often achieved through introducing a new safety measure that reduces the frequency of a hazardous accident rather than its consequences. To carry out a Jvalue analysis, it is necessary to calculate how a reduction in accident frequency extends the life expectancy of the potentially exposed group of people. The paper presents two methods for calculating the loss of life expectancy associated with accidents of a certain severity occurring with a defined frequency. The first begins by using an equivalent, prolonged radiation exposure to represent the effects of the accident occurring once per year over the given period of operation. The resultant loss of life expectancy is then scaled by multiplying by the frequency of occurrence. The second method calculates the loss of life expectancy brought about by a single accident occurring during the given period of operation and scales this by multiplying by both the length of the operational period and the frequency of occurrence. Results derived using the first method show that there is a relatively small effect on loss of life expectancy per accident if several accidents are assumed to occur during a typical period of operation. This conclusion permits a simple assessment of the effect of possible, multiple accidents. The accuracy of the second method is found not to be compromised materially by ignoring the possibility ofmultiple accidents. The second method is shown to be slightly more conservative than the first, and also somewhat more accurate. Calculations of the loss of life expectancy may be carried out before and after the new safety improvement has been implemented, and the difference between the two results will be the life extension brought about by the new safety measure.

10. Thomas, P. J. and Jones, R. D., 2009, "Calculating the benefit to workers of averting a prolonged radiation exposure for longer than the working lifetime", Trans IChemE, Part B, Process Safety and Environmental Protection, Vol. 87, 161 – 174.
The Jvalue method enables health and safety schemes aimed at preserving or extending life to be assessed on a common, objective basis for the first time, irrespective of industrial sector. For this it requires an estimate of the improvement in life expectancy that the health and safety scheme will bring about. This paper extends the range of nuclearsafetysystem lifetimes for which it is possible to calculate the increased life expectancy amongst nuclearplant workers whose radiation exposure the safety system has reduced. Whereas the previous mathematical technique was able to cater for a nuclearsafetysystem lifetime up to the working lifetime of the nuclearplant workers (typically between 45 and 50 years), the new method extends without limit the range of tractable, safety system lifetimes. This is important now that the design lifetime of nuclear power stations can be up to 60 years. The development will also facilitate the assessment of safety systems and procedures to protect workers on longterm nuclear decommissioning and waste sites; in the latter case, the service lifetime could be hundreds of years. The case when the safetysystem lifetime is greater than the working lifetime is addressed by splitting the workforce into a set of three cohorts, one for existing workers and two for new recruits. The discounted life expectancy is found for each cohort, and then a weighted average is used to give the overall value. An additional mathematical device is then used to reduce the number of cohorts required from three to two, namely existing workers and new recruits. A similar mathematical device is applied (in Appendix A) to reduce from three to two the number of workforce cohorts needed when the length of the safety system’s service lifetime is less than the working lifetime. Finally, a further mathematical instrument is incorporated in the model equations, which allows a unified treatment to be applied to each of the cohorts, existingworkers and newrecruits, across all possible service lifetimes of a nuclear safety system. Since newresults on gain in life expectancymay be fed into a Jvalue analysis, this development extends significantly the range of nuclearsafety systems for which the Jvalue technique may be used to measure costeffectiveness.

12. Thomas, P. J. and Jones, R. D., 2009, "Incorporating the 2007 recommendations of the International Committee on Radiation Protection into the Jvalue analysis of nuclear safety systems", Trans IChemE, Part B, Process Safety and Environmental Protection, Vol. 87, 245 – 253.
The newly released findings by the International Commission on Radiation Protection (ICRP) led to a review of the lifetime risk coefficients for fatal cancer used in Jvalue analysis of nuclear safety systems. The change in life expectancy a safety system brings about by averting a radiation exposure needs to be estimated in order to calculate the safety system's Jvalue, and this is done following the ICRP's practice of using risk coefficients that are uniform across both genders and all ages in the defined population group (either workers or the general population). The ICRP predicted uniformly lower radiation risks in 2007 than in 1990 on a likeforlike basis, but it was found that the ICRP's new risk coefficients needed to be multiplied by a compensating factor specific to each population when used in calculating the radiationinduced change in life expectancy. Incorporating the new compensating factor leads to a decrease in the Jvalue calculated of about 5% for workers and 15% for the general population compared with earlier, reported results. This will strengthen slightly the case for spending on a nuclear safety measure.

14. Thomas, P., Jones, R. and Kearns, J., 2009, "Measurement of parameters to value human life extension", Proc. XIX IMEKO World Congress, Fundamental and Applied Metrology, September 6–11, 2009, Lisbon, Portugal, pp 1170 – 1175.

17. Thomas, P. J., Jones, R. D. and Boyle, W. J. O., 2010a, "The limits to risk aversion: Part 1. The point of indiscriminate decision", Process Safety and Environmental Protection, Vol. 88, No. 6, November, pages 381 – 395.
The paper uses utility theory to investigate how much should be spent to avert all costs from an industrial accident apart from direct human harm. These “environmental costs” will include those of evacuation, cleanup and business disruption. Assuming the organisation responsible will need to pay such costs, the difference between its expected utility with and without an environmental protection system constitutes a rational decision variable for whether or not the scheme should be installed. The value of utility is dependent on the coefficient of relative risk aversion, “riskaversion” for short. A model of an organisation’s decisionmaking process has been developed using the ABCD model, linking the organisation’s assets, A, the cost of the protection scheme, B, the cost of consequences, C, and the expected utility difference with and without the scheme, D. Increasing the organisation’s riskaversion parameter will tend to make it less reluctant to invest in a protection system, but can bring about such investment only when the scheme is relatively close to financial breakeven. For such borderline schemes, the amount the organisation is prepared to spend on the protection system will rise as the riskaversion increases. The ratio of this sum to the breakeven cost is named the “Limiting Risk Multiplier”, the maximum value of which is governed by the maximum feasible value of riskaversion. However, the mathematical model shows that increasing the riskaversion will reduce the clarity of decision making generally. Although the reluctance to invest in a protection scheme may change sign and turn into a positive desire to invest as the riskaversion increases, the absolute value of this parameter is a continuously decreasing function of riskaversion, tending asymptotically to zero. As a result, discrimination will gradually diminish, being lost altogether at the “point of indiscriminate decision”. Here the decision maker will be able to distinguish neither advantage in installing the scheme nor disadvantage in installing its inverse. There is a close correspondence between this mathematically predicted state and that of panic, where an individual has become so fearful that his actions become random. The point of indiscriminate decision provides a natural upper bound for the value of riskaversion. This bounds the Limiting Risk Multiplier in turn, and so sets an objective upper limit on the amount that it is rational to spend on an environmental protection system.

18. Thomas, P. J., Jones, R. D. and Boyle, W. J. O., 2010b, "The limits to risk aversion. Part 2: The permission point and examples", Process Safety and Environmental Protection, Vol. 88, No. 6, November, pages 396 – 406.
Part 2 extends the analysis to show that it is possible to find the “permission point”, the value of (the coefficient of relative) riskaversion, at which decisions to sanction environmental protection are most likely to be made. The mathematical model describes the process by which the decision maker varies his riskaversion over a range of feasible values to find the riskaversion that will give him the greatest desire to invest in the protection system under consideration. If he can find such a riskaversion before losing discrimination (because the system is too expensive, given its performance), he will adopt it as his “permission point” and decide in favour of the expenditure. The permission point is, of course, bounded above by the point of indiscriminate decision. A maximum Risk Multiplier calculated at the point of indiscriminate decision may be applied to the protection expenditure at monetary breakeven to give the maximum, rational outlay on protection. Moreover, it is possible to model how the average UK adult should take decisions on protection to maximise his utility. Different situations will call for different values of riskaversion, which may explain why economists have come up with differing estimates of this parameter in the past. However, a central, average riskaversion may be calculated for the average UK adult as 0.85, which is within 4% of the value, 0.82, found from the newly reported method based on a tradeoff between income and future free time, and is consistent with several recent economic estimates. Worked examples assess how much an organisation should spend on a protection scheme to prevent accidents with very large environmental consequences.

25. Kearns, J. O. and Thomas, P. J., 2010, "Assigning tolerances to Jvalues used in safety analysis", Proc. 13th IMEKO TC1TC7 Joint Symposium Without Measurement no Science, without Science no Measurement, September 13, City University, London, UK, IOP Publishing, Journal of Physics: Conference Series 238 (2010) 012045. doi:10.1088/17426596/238/1/012045
This paper describes the methodology employed in the estimation of the input parameters required for Jvalue analysis. The conceptual foundations and theory behind Jvalue analysis are first presented, and the relevant parameters are derived. Evaluations of the parameters are then shown and their implications discussed, including an estimate of the coefficient of relative risk aversion, riskaversion for short. Uncertainties of the parameters are calculated. It is shown that the internal accuracy of the Jvalue is +/−4%, but that other external, casedependant effects may reduce this accuracy. Some of these casedependant sources of uncertainty are discussed and quantified.

28. Waddington, I., Boyle, W. J. O., Kearns, J., 2013, "Computing the Limits of Risk Aversion", Process Safety and Environmental Protection, 91, 92–100. doi:10.1016/j.psep.2012.03.003
Utility theory can be used to model the decision process involved in evaluating the costeffectiveness of systems that protect against a risk to assets. A key variable in the model is the coefficient of relative risk aversion (or simply “riskaversion”) which reflects the decision maker's reluctance to invest in such safety systems. This reluctance to invest is the scaled difference in expected utility before and after installing the safety system and has a minimum at some given value of riskaversion known as the “permission point”, and it has been argued that decisions to sanction safety systems would be made at this point. As the cost of implementing a safety system increases, this difference in utility will diminish. At some point, the “point of indiscriminate decision”, the decision maker will not be able to discern any benefit from installing the safety system. This point is used to calculate the maximum reasonable cost of a proposed safety system. The value of the utility difference at which the decision maker is unable to discern any difference is called the “discrimination limit”.
By considering the full range of accident probabilities, costs of the safety system and potential loss of assets, an average riskaversion can be calculated from the model. This paper presents the numerical and computational techniques employed in performing these calculations. Two independent approaches to the calculations have been taken, the first of which is the derivativebased secant method, an extension of the referred derivative method employed in previous papers. The second is the Golden Bisection Method, based on a Golden Section Search algorithm, which was found to be more robust but less efficient than the secant method. The average riskaversion is a function of several key parameters: the organisation's assets, the probability and maximum cost of an incident, and the discrimination limit. An analysis of the sensitivity of the results to changes in these parameters is presented. An average riskaversion of 0.8–1.0 is found for a wide range of parameters appropriate to individuals or small companies, while an average riskaversion of 0.1 is found for large corporations. This reproduces the view that large corporations will be risk neutral until faced with risks that pose a threat to their viability.