The limits to risk aversion: Part 2: The permission point and worked examples

Part 2 extends the analysis to show that it is possible to find the “permission point”, the value of (the coefficient of relative) risk-aversion, 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 risk-aversion over a range of feasible values to find the risk-aversion that will give him the greatest desire to invest in the protection system under consideration. If he can find such a risk-aversion 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 break-even 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 risk-aversion, which may explain why economists have come up with differing estimates of this parameter in the past. However, a central, average risk-aversion 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 trade-off 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.     

Computing the limits of risk aversion

Utility theory can be used to model the decision process involved in evaluating the cost-effectiveness of systems that protect against a risk to assets. A key variable in the model is the coefficient of relative risk aversion (or simply “risk-aversion”) 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 risk-aversion 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 risk-aversion 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 derivative-based 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 risk-aversion 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 risk-aversion of 0.8–1.0 is found for a wide range of parameters appropriate to individuals or small companies, while an average risk-aversion 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.     

Extending the J-value framework for safety analysis to include the environmental costs of a large accident

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.     

陆上油气管道受高压直流接地极干扰的腐蚀与防护实例分析

高压直流接地极放电时会对附近的管道产生强烈的电干扰,导致管道腐蚀加速,为了预测高压直流接地极对埋地管道的干扰程度并及时筛选合适腐蚀防护措施,利用数值模拟技术计算高压直流干扰下管道的干扰电位以及管体腐蚀速率,并结合相关标准对干扰水平进行评估。在此基础上,研究“单独管道方采取措施”、“管道方和电力方均采取措施”、“电力接地极更换极址”3种方案下的腐蚀防护效果。研究结果表明:对当前极址来说,需要管道方安装大量措施同时电力方对放电电流进行控制才能达到目标;而高压直流接地极极址土壤电阻率较低的情况下可以大幅降低对附近管道的干扰水平;就本文所列工程案例来说,更换极址是比较经济的方案。     

Pitfalls in the application of utility functions to the valuation of human life

Safety strategies in the process and other industries depend ultimately on how much the owners and operators decide should be spent on protection systems to protect workers and the public from potential plant hazards. An important input to decisions of this sort is the value of life, which needs to be assessed in a valid manner so that safety decisions can be made properly. A key reference point for decisions on safety investment decisions in the UK is a 1999 study on the “value of a prevented fatality” (VPF), which employs a two-injury chained model that has been shown previously by the present authors to possess internal inconsistencies. The 1999 study made extensive use of utility functions to interpret survey data, and it is this feature that is explored in this paper. It will be explained here how different forms of utility function of the Exponential family can produce the same figure for an intermediate parameter in the calculation of the VPF from the two-injury chained model. Exponential utility functions are, however, unlikely to provide a realistic representation if their calculated risk-aversions need to be negative or zero in order to match survey data, which would imply an incautious attitude amongst those taking decisions on safety. The use of an incompletely specified wealth threshold in the utility modelling is explored in the light of a proposal by the authors of the 1999 study that a second utility function can be used to determine the individual's utility when his wealth lies below the threshold, which constitutes the lower limit of validity of the first utility function. The proposition is shown to be untenable. The results presented in this paper raise further concerns about the lack of validity of the 1999 study on which the UK VPF is based and hence on the safety decisions that have been made in consequence.     

Investing in safety an analytical precautionary principle

PROBLEM: Governments and businesses must respond to increasing safety requirements and balance the associated costs with productivity and competing pressures. METHOD: A real options approach has been introduced for decision making in the private sector; this approach is adapted for regulatory decisions that can involve irreversible and uncertain safety impacts, social costs that differ from private costs, and differences in perception among the stakeholders. RESULT AND IMPACT ON INDUSTRY AND GOVERNMENT: The outcome is an economic decision gage that determines if it is optimal to invest in safety even if the estimated costs significantly exceed the estimated benefits. Applications potentially include safety decisions related to aviation, ground transportation, pipelines, nuclear facilities, natural disaster planning, and terrorism, among others.     

基于模糊逻辑理论的应急决策冲突程度表示方法研究

针对突发灾害事故应急决策过程中的冲突问题,提出1种应急决策冲突程度的表示方法,将应急决策冲突定量表示出来。基于模糊逻辑理论对应急决策冲突进行模糊评价;通过构建“大多数”的模糊函数,确定冲突程度的表示路径;根据冲突与一致性的相对关系,对“一致性程度”的模糊函数进行改造,构建“冲突程度”的模糊函数,并通过冲突程度的计算过程,得到最终的冲突程度;结合应急决策冲突实际,划分冲突等级,并确定其取值范围。研究结果表明:基于模糊逻辑理论的应急决策冲突程度表示方法充分利用了应急决策专家的决策偏好信息,实现了应急决策冲突程度的定量表示。     

Safety and Cost-Effectiveness of Clearzones in Rockcuts

Clearzones are a feature of modern highways that have a dramatic impact on roadside safety. The purpose of these unobstructed spaces is to provide an area where an errant vehicle can safely stop or the driver can regain control of the vehicle without striking a hazardous object like a tree or utility pole. Many clearzone alternatives (e.g., removing trees, installing traversable culvert openings, and installing guardrails in front of untraversable hazards) are relatively inexpensive in comparison to other roadway construction costs. Roadways passing through rockcuts present an unusual case where the construction cost of providing the clearzone is very high. This article examines different clearzone alternatives in rockcuts and compares the likely effect on safety and construction costs. A method is described for determining the rockcut width that best balances the cost of construction with the improvements in safety that would result from a wider clearzone in the rockcut.     

Testing the validity of the “value of a prevented fatality” (VPF) used to assess UK safety measures

The “value of a prevented fatality” (VPF), the maximum amount that it is notionally reasonable to pay for a safety measure that will reduce by one the expected number of preventable premature deaths in a large population, is published by the UK Department for Transport (DfT). The figure, updated for changes in GDP per head, is used by the DfT, the Health and Safety Executive and other UK regulatory bodies as well as very widely in the process, nuclear and other industries as the standard by which to judge how much to spend to reduce harm to humans. The paper tests the validity of the 1999 study on which the VPF is based and finds that that study fails numerous tests of its validity. It is concluded that there is no evidential base for the VPF that has been used for many years in the UK and is still in standard use today. Given the difficulties evident in the interpretation of survey results, an urgent re-appraisal is needed of alternative statistical methodologies that can allow robust regulatory and industry safety decision making and, vitally, give adequate protection to the UK public and to those working in the UK's transport, process, nuclear and other industries.     

J-value analysis of different regulatory limits for workers and the public

The J-value technique allows an objective determination to be made of the resources that should be applied cost effectively to improve heath and safety. This is essential if capabilities are to be employed optimally and risks reduced in a way that reflects their severity. Although other considerations such as good practice and socio-political influences may affect a final decision on the resources to be sanctioned, the incorporation of these additional factors should be made transparent if the decision is no longer to be based on cost effectiveness. The J-value provides an objective criterion by which to judge when “reasonable practicability” has been achieved in committing resources for safety improvement, which is the legal requirement under health and safety law in the UK.Moreover, the J-value methodology also allows other related issues to be addressed objectively. Regulatory bodies apply different limits for workers and the general public, with higher risks being permitted for workers. Although a factor of about 10 has been used in several contexts, no objective rationale has been developed for this particular figure until now. However, it is shown that application of the J-value analysis can provide a justification for a ratio of workers’ risk to public risk of approximately this size if certain reasonable assumptions are made. Thus the paper provides the first quantitative explanation for the different levels of protection demanded by regulators nationally and internationally for workers and public.     

铁路危险货物办理站点优化配置方法研究

铁路危险货物运输办理站点的优化配置,涉及到需求分布、设置地点、区域规划、环保要求、业务功能以及与其他运输方式的分工、衔接等,是一个复杂的系统工程。分析了已有铁路危险货物办理站点整合优化模型的不足,首先从铁路部门角度综合考虑现有铁路危险货物办理站点的各方面条件,进行多准则决策评价,从运输需求者角度考虑运输方式多属性决策,进行铁路危险货物办理站点的综合效用评价,并基于投资成本、环境风险、运输效用和区域公平性等方面构建了铁路危险货物办理站点优化配置模型,为了有效解决多站点、多需求、多区域、多目标铁路危险货物办理站点优化配置模型因素复杂、规模大、层次多的问题,提出了运用大系统分解协调的多目标遗传算法求解模型的思路。     

Analyzing system safety and risks under uncertainty using a bow-tie diagram: An innovative approach

A bow-tie diagram combines a fault tree and an event tree to represent the risk control parameters on a common platform for mitigating an accident. Quantitative analysis of a bow-tie is still a major challenge since it follows the traditional assumptions of fault and event tree analyses. The assumptions consider the crisp probabilities and “independent” relationships for the input events. The crisp probabilities for the input events are often missing or hard to come by, which introduces data uncertainty. The assumption of “independence” introduces model uncertainty. Elicitation of expert's knowledge for the missing data may provide an alternative; however, such knowledge incorporates uncertainties and may undermine the credibility of risk analysis.This paper attempts to accommodate the expert's knowledge to overcome missing data and incorporate fuzzy set and evidence theory to assess the uncertainties. Further, dependency coefficient-based fuzzy and evidence theory approaches have been developed to address the model uncertainty for bow-tie analysis. In addition, a method of sensitivity analysis is proposed to predict the most contributing input events in the bow-tie analysis. To demonstrate the utility of the approaches in industrial application, a bow-tie diagram of the BP Texas City accident is developed and analyzed.     

橇装式 LNG 汽车加气站防雷安全研究

橇装式LNG汽车加气站作为新型加气站的一种,其一旦发生雷击并引发火灾或爆炸将造成不可估量的损失,因此橇装式LNG汽车加气站的防雷安全十分重要。在结合橇装式LNG汽车加气站所处环境及其系统特点,雷电对其破坏机理和途径,分析了造成雷电灾害因子。通过计算分析,运用ADBSGP现代综合防雷技术从防直击雷、防闪电感应、防雷击电磁脉冲等方面入手,提出了安装外部防雷装置、采用防雷等电位连接技术作为防闪电感应措施,采取屏蔽和安装SPD作为防雷击空间电磁场和闪电电涌侵入措施。     

Self‐protective reactions to peer abusive supervision: The moderating role of prevention focus and the mediating role of performance instrumentality

Across 3 studies, we apply a self‐protection perspective of observed mistreatment to examine a moderated mediation model on “when” and “why” third parties are motivated by peer abusive supervision. We hypothesize that prevention‐focused third parties will increase their performance effort as a response to peer abusive supervision, and this effect is mediated by performance instrumentality. In a field study of working adults (Study 1) and an experimental study that manipulated peer abusive supervision (Study 2), we found that peer abusive supervision interacted with third parties' prevention focus to predict their performance effort such that peer abuse was positively related to third parties' performance effort only for those high on prevention focus. Results were replicated in a second field study of working adults (Study 3). Further, we found support for the mediating effect of performance instrumentality. The theoretical and practical implications of our results are discussed.     

3-Parameters SPW technique: A new method for evaluation of target safety integrity level

Introduced by IEC-61508 standard, safety integrity levels (SIL) have been used for assessing the reliability of safety instrumented functions (SIF) for protection of the system under control in abnormal conditions. Different qualitative, semi-qualitative and quantitative methods have been proposed by the standard for establishing target safety integrity levels amongst which “Risk Graph” has gained wide attention due to its simplicity and easy-to-apply characteristics. However, this method is subject to many deficiencies that have forced industry men and experts to modify it to fit their demands. In this paper, a new modification to risk graph parameters has been proposed that adds more flexibility to them and reduces their subjective uncertainties but keeps the method as simple as before. Three parameters, namely severity (S), hazard avoidance probability (P), and demand rate (W) are used instead of former four parameters. Hence, the method is named SPW. The outcome results of this method can be directly converted to probability of failure on demand (PFD) or risk reduction factor (RRF). The proposed method has been tested on an example case that has been studied before with conventional risk graph and LOPA techniques. The results show that new method agrees well with LOPA and reduces costs imposed by conservative approximations assumed during application of conventional risk graph.     

Safety compliance climate concerning risk assessment and preventive measures in EU legislation: A Finnish survey

The aim of the present study is to explore the process dynamics of the safety compliance climate and work relationships, including their antecedents and consequences. After investigating the many dimensions of safety compliance climate and of work relationships, the study concludes that a multi-component measure is needed to fully assess all of their dimensions. With respect to the impacting positively on safety compliance legislation, the present study found the following factors: “contribution measures”, “concrete preventive measures” and “risk assessment process”. For risk assessment factors on safety compliance the study identified “planning, guidelines, policy, management”, “prioritization of proactive measures”, “results in cooperation and information” and “active use of risks assessment document”. In a regression model for the workers, both risk assessment process and contribution measures had a statistically highly significant (p < 0.001) effect on concrete preventive measures. In the regression analysis of the employers risk assessment process had a statistically significant (p < 0.01) effect and contribution measures had a statistically highly significant (p < 0.001) effect on concrete preventive measures.     

A case study: An explosion in a milk spray dryer,CAPSA, NW Spain

European Standard EN 14491 (2006): “Dust explosion venting protective systems”, based on German Standard VDI 3673 (2002): “Pressure venting of dust explosions”, Verein Deustcher Ingenieure, specifies the basic design requirements for the selection of dust explosion venting protection systems.In this study an investigation into the efficiency of venting surfaces in accordance with Standard EN 14491 has been undertaken to check the validation of the same. Thus, the application of the standard to an actual case of an explosion in a milk spray dryer has been studied, taking into consideration the explosive characteristics of products treated in this type of installation and their venting requirements.The results obtained indicate that, in specific situations – such as the effects of turbulence, particularly in the cone, or dust layer self-ignition – the European Standard could underestimate the venting surface requirements needed to alleviate possible excess internal pressure in order to avoid injury or structural damage to spray dryers.     

突发事件应急决策模拟演练设计理论框架与技术要点

突发事件应急决策模拟演练是提升参演主体应急处置能力的重要途径，该类演练的设计开发需要系统性的理论与技术进行规范和引导。从实践归纳的角度，将该类演练的设计划分为演练内容设计和演练形式开发2部分，详尽地分析演练内容设计中的4个核心要素（主题与目标、演练情景、演练任务和目标能力）和演练形式开发中的3项关键技术（控制流程、任务导入与方案输出、信息技术平台）。此外，着重介绍了突发事件应急决策模拟演练设计开发过程中容易混淆的几组概念关系，即“情景构建与应急演练的关系”、“应急预案与应急演练的关系”、“演练内容与演练形式的关系”、“演练中‘演’与‘练’的关系”。     

Safety is an inherently inconsistent concept

Some basic principles for philosophical definition work are introduced and then applied to safety and related concepts. Definitions are provided first for comparative safety concepts such as “safer than” and then for the monadic “safe”. It is shown that “safe” is an inherently inconsistent concept, i.e. it cannot be restored to consistency without giving up what we perceive as some of its central elements. The reason for this is that both absolute and relative conceptions of safety are entrenched in common usage of the term. In order to avoid the inconsistency a strategy of terminological ramification is proposed: We should distinguish between the two concepts “reasonably safe” and “absolutely safe”. Any usage of “safe” or “safety” simpliciter should be seen as an abbreviated reference to one of these two closely related, remarkably confusable, but still unmergable concepts.     

Analyzing the safety impact of longer and heavier vehicles circulating in the European market

Introduction: The European Union (EU) has developed different strategies to internalize the costs of excessive motor traffic in the road freight transport sector. One of these is a relaxation of restrictions on the size and load capacity of trucks that circulate between member States and a proposal has been made for Longer and Heavier Vehicles (LHVs) to be allowed to circulate across borders. LHVs are the so-called “megatrucks” (i.e., trucks with a length of 25 meters and a weight of 60 tonnes). Megatrucks have allowed to circulate for decades in some European countries such as Norway, Finland, and Sweden, world leaders in traffic accident prevention, although the impact that cross-border traffic would have on road safety is still unknown. Methods: This article provides an econometric analysis of the potential impact on road safety of allowing the circulation of “megatrucks” throughout the EU. Results: The findings show that countries that currently allow megatrucks to circulate present lower traffic accident and fatality levels, on average. Conclusions: The circulation of this type of vehicle is only advisable in countries where there is a certain degree of maturity and demonstrated achievements in the field of road safety. Practical applications: European countries that have allowed megatruck circulation obtaining better road safety outcomes in terms of accidents, although the accident lethality rate seems to be higher. Consequently, introducing megatruck circulation requires a prior proper preparation and examination.