J-value

judging the risk

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Core Ideas

The following papers draw together the key concepts and methodology of the J-value.

• 1. Thomas, P. J., Stupples, D. W., and Alghaffar, M. A., 2006a, "The extent of regulatory consensus on health and safety expenditure. Part 1: development of the J-value technique and evaluation of the regulators' recommendations", Process Safety and Environmental Protection, 84(5), 329–336. doi: 10.1205/psep05005

  The new J-value technique is developed from a life-quality index that is a function of life expectancy, average income and work-life balance. The method is used to assess the degree of consensus on health and safety expenditure amongst regulators across different sectors of the economy. A measure of agreement is found in the regulator's theoretical recommendations.

• 2. Thomas, P. J., Stupples, D. W. and Alghaffar, M. A., 2006b, "The extent of regulatory consensus on health and safety expenditure. Part 2: Applying the J-value technique to case studies across industries.", Process Safety and Environmental Protection, 84(5), 337–343. doi: 10.1205/psep05006

  The measure of agreement in the regulator's theoretical recommendations found by using the J-value technique is contrasted with the very large disparities found on practical health and safety schemes. The J-value method is proposed as a common yardstick for assessing health and safety spend for the use of decision makers in all sectors. Its adoption could lead to better targeting of health and safety spend in all areas of the economy.

• 3. Thomas, P. J., Stupples, D. W., and Alghaffar, M. A., 2006c, "The life extension achieved by eliminating a prolonged radiation exposure", Process Safety and Environmental Protection, 84(5), 344–354. doi: 10.1205/psep05007

  A key parameter for evaluating the worth of safety equipment is the extension to life expectancy that it brings about in the population it is intended to protect. Since this is numerically equal to the decrease in life expectancy that would occur were the equipment not there, its value may be calculated by estimating the effect of the prolonged radiation exposure that would occur in the equipment's absence. This paper describes a procedure for carrying out this computation efficiently for cost-benefit studies using the J-value method.

• 4. Thomas, P. and Stupples, D., 2006, "J-value: a universal scale for health and safety spending", Special Feature on Systems and Risk, Measurement + Control, Vol. 39/9, 273 – 276, November.

  A common yardstick against which to judge spending on health and safety across all sectors of the economy is needed if resources are not to be diverted away from areas of greater need. It is argued that the J-value is an objective, absolute and universal scale that fulfils that need. Previous judgments on the value for human life are reproduced, but the J-value demonstrates that significant differences exist currently in the regulatory standards for different industries. Case studies show that very different levels of health and safety spend have been demanded in practice in those industries.

• 5. 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, 140 – 145.

• 13. Kearns, J.O., 2009, "The trade-offs embodied in J-value analysis", Universities' Nuclear Technology Forum, UNTF 2009, March 18 – 20 2009, Cambridge, UK.

• 16. Thomas, P. J., Kearns, J. O. and Jones, R. D., 2010, "The trade-offs embodied in J-value safety analysis", Process Safety and Environmental Protection, 88(3), 147–167. doi: 10.1016/j.psep.2010.02.001

  The paper presents a new derivation of the J-value method for assessing health and safety expenditure that highlights the fact that two trade-offs are involved. The trade-off between safety spend and the resulting improvement in life expectancy rests on a prior trade between free-time fraction and income, made at a societal level. It is suggested that each trade is a specific instance of a more general exchange between expected free-time and income, and that the terms of the trade-off are similar, so that the percentage increase in life expectancy has the same value as a similar percentage increase in total expected free-time. The theoretical framework suggests that the average person values all his time equally, but perceives that he has sold his expected working time to an employer, so that, while he will still place a value on it, he does not see that value as coming to him, but rather going to his employer in exchange for the compensation he is being paid. Thus he values the extra years of life expectancy he obtains from a health and safety measure solely in terms of the extra years of free-time he expects to gain. The value of the exponent in the life-quality index has been shown to be equal to both the modulus of the elasticity of expected future free-time with respect to income and the modulus of the elasticity of life expectancy with respect to income. The indifference curves on the planes of income versus life expectancy and income versus discounted life expectancy have been shown to be the loci of J = 1. The actuarial basis for the calculation of working time fraction to the end of life has been explained, and data on the share of wages in Gross Domestic Product have been discussed. Based on recent statistics from the UK economy, the average person would be prepared to forego about 5½% of his income to the end of life in order to increase his life expectancy or discounted life expectancy by 1%, and would require his lifetime income to be increased by 5½% to compensate him for a loss of 1% in his life expectancy, discounted or otherwise. A small degree of asymmetry will, however, occur for larger percentage changes in life expectancy, with the average person requiring somewhat more compensation for a loss of life expectancy than he is prepared to pay for a gain.

• 19. Thomas, P. J. and Jones, R.D, 2010, "Extending the J-value framework for safety analysis to include the environmental costs of a large accident", Process Safety and Environmental Protection, Vol. 88, No. 5, September, pages 297 – 317.

  A severe accident on an industrial plant has the potential to cause, in addition to human harm, general damage and hence expense, associated with ground contamination, evacuation of people and business disruption, for example. The total cost of damages, given the name “environmental costs” in this paper,may be comparable with or larger than the cost of direct health consequences, as assessed objectively by the J-value approach. While the low probability of the accident may mean that the expectation of monetary loss is small, the paper develops a utility-based approach to determine how much should be spent on protection systems to protect against both environmental costs and human harm. The behaviour of the fair decision maker in an organisation facing possible environmental costs is represented by an Atkinson Utility function, which is dependent on the organisation’s assets and on the elasticity of marginal utility or, equivalently, the coefficient of relative risk aversion, “risk-aversion” for short. A Second Judgment Value, J₂, may be derived from the spend on the protection system after subtracting the amount sanctioned to prevent direct human harm. This net, environmental expenditure is divided by the most that it is reasonable to spend to avert environmental costs at the highest, rational risk-aversion. The denominator in this ratio is found by first calculating the maximum, sensible spend at a risk-aversion of zero, and then multiplying this figure by a Risk Multiplier to give the maximum, fair amount to avert environmental costs. The Risk Multiplier incorporates a risk-aversion that is as large as it can be without rendering the organisation’s safety decisions indiscriminate and hence random. An overall, Total Judgment Value, the J_T-value, may also be calculated, which takes into account the reduction in both human harm and environmental cost brought about by the protection system. The new J_T-value will show similar behaviour to the original J-value, in that J_T-values up to unity will indicate reasonable value for money, while J_T-values greater than unity will indicate a prima facie overspend on protection that will need to be justified by further argument. While the analysis is phrased in terms of environmental costs, the treatment is sufficiently general for all costs, including onsite damages, loss of capability etc. to be included. The new, J_T-value method provides for a full and objective evaluation of the worth of any industrial protection system. A worked example is given.

• 20. Thomas, P., "Extending the J-value into environmental protection as well as safety", 2010, Hazards Forum Newsletter 66 – Spring, pages 8 – 10.

• 21. Thomas, P., Jones, R. and Kearns, J., 2010, "J-value safety assessment: the two trade-offs", Measurement + Control, Vol. 43, No. 5, June, pages 142 – 145.

  In physics and engineering, we are fortunate in having a whole body of widely accepted learning on the governing laws. Von Neumann and Morgenstern noted 60 years ago that this happy situation did not carry over to socio-economic theory, and while undoubtedly there has been major progress since then, there remain many areas where fully satisfactory theories have still to be developed. Here, as in engineering, the development of a workable mathematical model is the first priority, since it is only in this way that we can identify the parameters that need to be measured and calculated.

• 22. Thomas, P. and Jones, R., 2010, "J_T-value assessment of schemes to protect against accidents with high human and environmental costs", Measurement + Control, Vol. 43, No. 5, June, pages 152 – 155.

  Society will continue to demand ever higher levels of safety for humans and protection for the environment as civilisation advances. But economic resources will always be limited as there will always be other things that, quite properly, people will want to do. So what is needed is an objective answer on how much ought to be spent on safeguards. Building on the work of Nathwani, Pandey and Lind, such an answer has been made available in the J-value for protection schemes that reduce the risk to human life. But while human harm may be the predominant risk in some cases, very often an industrial protection system will be designed to mitigate also against other economic and environmental costs. For example a shut-down system on a chemical plant or a nuclear reactor will protect against not only human harm but also damage to nearby plant and the spread of contamination to the environment.

  For brevity, we shall refer to the costs associated with environmental clean-up, evacuation of people, loss of business, damage to plant and damage to reputation as "environmental costs", with the understanding that other costs may be brought under this umbrella in some cases. The trade-off between extra spending on the protection system and these environmental costs may be quantified using utility theory, and the result integrated with the J-value to produce a J_T-value (total judgement value), which will indicate whether the total cost of the protection system is reasonable in view of its ability to protect both humans and the environment. The application of utility theory in this case may be achieved through using the ABCD model.

• Thomas, P. J., 2012, "Discount rates for use in calculating the J-value", Life Quality Index Symposium, Joint Committee on Structural Safety, August 21–23, Technical University of Denmark, Lyngby, Denmark. Download PDF.

  The Life Quality Index (LQI) and the J-value use discount rates in two contexts: (i) to discount the utility of the individual's future earnings and (ii) to discount costs and benefits from schemes that have societal benefit. The former is termed the "net discount rate" while the latter is termed the "social discount rate", and used to convert the stream of costs that is reasonable for a protection scheme at a J-value of unity into a single, up-front figure. The net discount rate is shown to depend on the three parameters: the pure time discount rate, the nation's growth rate, and the average person's risk-aversion. An appeal is then made to Ramsey's economic model, and a derivation of Ramsey's result is given, which links the social discount rate to the same three parameters. It is then established that the net discount rate is equal to the social discount rate minus the rate of growth of Gross Domestic Product. The difficulties associated with the subjectivity of the pure time discount rate are discussed, but these may be bypassed in the UK context if the Treasury-recommended value for the social discount rate is accepted. Accepting the Treasury's view on the UK's average growth rate also then enables the net discount rate to be found by subtraction.

  Different countries will experience different conditions, particularly for growth rate. Nevertheless the mathematical framework developed in this paper may be used to estimate appropriate figures for those countries.

• Faber, M. H., Lind, N., Nathwani, J., Thomas, P., Vrouwenvelder, T., 2012, "A Common Rationale for Health and Life Safety Management", High Level Risk Forum, December 13–14, Organisation for Economic Co-operation and Development, Paris, France.

  In this paper, we provide a rationale for decision-making to enhance life safety that takes into full account the limitations and constraints of available resources. Maximizing life safety for all is a desirable goal but we need to acknowledge that the "safe" and the "dangerous" are inextricably intertwined in all human activities. We propose the marginal life saving principle together with the Life Quality Index (LQI) as a basis for supporting transparent decision making across all sectors at national and global scales; spanning over risk management related to natural hazards, industrial accidents, traffic safety, over nuclear incidents to development aid and disease control. The approach outlined here is practical and meets the requirements of fundamental human values as it relates to enhanced safety of individuals and it allows an explicit balancing of risk reduction with life saving benefits.

• Thomas, P. J., Vaughan, G. J., 2013, "All in the balance: assessing schemes to protect humans and the environment", Nuclear Future, May/June, 9(3), 42 – 51.

  How safe is safe enough? Philip Thomas and Geoff Vaughan consider how to take a rational approach to safety assessment and ways to determine appropriate spending on safety.

  Events will always be diffcult to deal with, and this will be particularly true of accidents, hopefully of low frequency, that lead to loss of life and millions or billions of pounds worth of damage. The J-value and J_T-value, for schemes to protect, respectively, humans and both humans and the environment, provide objective metrics that can be used as a consistent guide for decision makers. Their use does not preclude the decision-maker from spending more money than would be implied by these measures. He might be inclined to do so when he has additional concerns in the socio-political area, for example. However, the availability of the J-value and/or J_T-value will provide a consistent platform on which to base the ultimate decision and to explain it if called upon to do so.

• Thomas, P. J., 2013, "The importance of risk-aversion as a measurable psychological parameter governing risk-taking behaviour", Joint IMEKO TC1-TC7-TC13 Symposium, J. Phys.: Conf. Ser., 459, 012052. doi:10.1088/1742-6596/459/1/012052

  A utility function with risk-aversion as its sole parameter is developed and used to examine the well-known psychological phenomenon, whereby risk averse people adopt behavioural strategies that are extreme and apparently highly risky. The pioneering work of the psychologist, John W. Atkinson, is revisited, and utility theory is used to extend his mathematical model. His explanation of the psychology involved is improved by regarding risk-aversion not as a discrete variable with three possible states: risk averse, risk neutral and risk confident, but as continuous and covering a large range. A probability distribution is derived, the "motivational density", to describe the process of selecting tasks of different degrees of difficulty. An assessment is then made of practicable methods for measuring risk-aversion.

• Thomas, P. J., 2013, "Methods for measuring risk-aversion: problems and solutions", Joint IMEKO TC1-TC7-TC13 Symposium, J. Phys.: Conf. Ser., 459, 012019. doi:10.1088/1742-6596/459/1/012019

  Risk-aversion is a fundamental parameter determining how humans act when required to operate in situations of risk. Its general applicability has been discussed in a companion presentation, and this paper examines methods that have been used in the past to measure it and their attendant problems. It needs to be borne in mind that risk-aversion varies with the size of the possible loss, growing strongly as the possible loss becomes comparable with the decision maker's assets. Hence measuring risk-aversion when the potential loss or gain is small will produce values close to the risk-neutral value of zero, irrespective of who the decision maker is. It will also be shown how the generally accepted practice of basing a measurement on the results of a three-term Taylor series will estimate a limiting value, minimum or maximum, rather than the value utilised in the decision. A solution is to match the correct utility function to the results instead.

• Thomas, P., 2014, "The J-value framework for determining best use of resources to protect humans and the environment", invited lecture at the First International Conference on Structural Integrity (ICONS-2014), February 4-7, 2014, Kalpakkam, India. Download PDF.

  The philosophy of the ALARP principle (as low as reasonably practicable) will be discussed, which has been adopted as the basis for UK law on health and safety. It will be shown how ALARP leads naturally to a need for cost-benefit analysis but how there are particular difficulties in the valuation of human life. The problems with the VPF concept ("value of a prevented fatality") will be explained, and the advance brought about by the Life Quality Index highlighted. The J-value (J for Judgement) will be introduced as a single metric for deciding whether the money being spent to reduce a risk to human life is rational or not. Expenditure up to a J-value of unity is reasonable. Then a second Judgement Value, the J₂₀-value, will be described, which may be combined with the J-value to give the Total Judgement value or J_T-value. Spending up to a J_T-value of unity is reasonable to safeguard humans and the environment.

• Thomas, P., 2016, "Measuring risk-aversion: The challenge", Measurement, 79, 285–301. doi: 10.1016/j.measurement.2015.07.056

  Risk-aversion is advanced as a measure of the feeling guiding the person who faces a decision with uncertain outcomes, whether about money or status or happiness or anything else of importance. The concepts of utility and, implicitly, risk-aversion were used first nearly 300 years ago, but risk-aversion was identified as a key dimensionless variable for explaining monetary decisions only in 1964. A single class of utility function with risk-aversion as sole parameter emerges when risk-aversion is regarded as a function of the present wealth, rather than subject to alteration through imagining possible future wealths. The adoption of a single class allows a more direct analysis of decisions, revealing shortcomings in the use of conventional, Taylor series expansions for inferring risk-aversion, over and above the obvious restrictions on perturbation size. Dimensional analysis shows that risk-aversion is a function of three dimensionless variables particular to the decision and a set of dimensionless character traits, identified later as the limiting reluctance to invest and the lower threshold on risk-aversion. The theoretical framework presented allows measurement of risk-aversion, paving the way for direct, evidence-based utility calculations.

• Thomas, P., and Waddington, I., 2019, "Fallacies in criticisms of the J-value", Process Safety and Environmental Protection, Vol. 126, 309–328. Available here

  Detailed examination of the criticisms of the J-value put forward by Jones-Lee and Chilton shows their points to be without merit. However, the exercise of refuting their critique has brought out a number of J-value implications of potential interest and value to engineering professionals seeking to find the objectively reasonable amount that ought to be spent on a safety system. The paper applies the J-value to the example of a long-term protection system on a notional major-hazard process plant, where a severe accident would otherwise pose a risk of death to the general public either immediately or in the short term. Equations are developed for the improvement in life expectancy produced by averting such an industrial hazard over a prolonged period. The opportunity is taken to review the developments in the J-value that have taken place over the 12 years since the first paper on the method appeared in Process Safety and Environmental Protection.

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