It is now over a year since Fukushima in Japan suffered the combined force of the Tohoko earthquake and subsequent tsunami and the world’s attention fell on the stricken Daiichi nuclear power plant there. The twin disasters hit on the 11th of March 2011. Initially, when the earthquake hit, the active reactors, numbers 1, 2 and 3, were all safely shut down. However, the impact of the closely-following tsunami took out the electrical power which was being used to cool the reactors. The backup cooling was lost later the same day which led to the meltdown of the 3 reactors and the release of radioactive substances initially into the air and then later into the sea. A 20km evacuation zone was quickly established around the plant and is still in place today.
The disaster has been widely seen as the most serious since Chernobyl in 1986 and was rated at 7, the most serious level denoted as “major accident”, on the International Nuclear and Radiological Event Scale, which was designed to explain the significance of nuclear events.
The accident at Fukushima, in the days after the disaster, caused an increase in public apprehension surrounding nuclear power in countries around the world. Resulting demonstrations took place in nations as diverse as France, Germany, India, Spain and Taiwan. Faced with this backlash of public opinion many countries’ politicians also temporarily lost their faith in nuclear power. Germany closed 7 of its oldest reactors for three months, Italy postponed a referendum on building a new generation of new plants (this still hasn’t taken place) and South Korea announced $1 billion of investment into the safety of its existing plants. Such reactions were not surprising; nuclear power is both an emotive and controversial subject. However, a year on, and with the initial furore having died down, it seems sensible to ask some questions around the area of nuclear power.
1. How much of our current electricity comes from nuclear power?
2. How much of our future electricity is likely to come from nuclear power?
3. What is currently done to ensure the safety of nuclear power plants?
The answer to the first question varies greatly from country to country. In 2010 the percentages of electricity being generated by nuclear facilities in the UK and USA were 15.66% and 19.59% respectively (http://www.iaea.org/). Note that this is not the percentage of nuclear power used in each country. The UK is by no means the most prolific nuclear generating nation, however. Over a quarter of the electricity generated in Japan and Sweden comes from nuclear and in France the figure is 77.71%.
Overall the picture over the last twenty or so years has been one of a steady increase in the world’s civil nuclear capabilities. Figure 1 shows the worldwide capacity (in GW) of nuclear power between 1991 and 2010 based on data from the International Atomic Energy Agency.
Figure 1: Worldwide capacity of nuclear power (in GW) between 1991 and 2010.
We see a steady increase in the capacity over the period, which has perhaps slowed slightly over the past five or so years. Of course all of these data are prior to the Fukushima disaster and subsequent temporary loss of confidence in nuclear power. Figure 2 indicates the total worldwide energy supplied by nuclear power over the same period.
Figure 2: Worldwide energy supplied by nuclear power (in Tw.h) between 1991 and 2010.
The trend is broadly the same, although there is a distinct levelling out of the usage over the last 8 or so years. This leads us nicely on to our second question: what does the future hold for nuclear power? We shall consider the answer to this for the case of the UK initially.
The UK government has just announced a new joint policy with France aimed at closer co-operation in the area of nuclear power. At the heart of this is a deal worth £400 million involving Rolls Royce and Areva for new nuclear reactors at sites in the two nations. In all eight sites in the UK are currently under consideration for new nuclear power reactors; Bradwell in Essex, Hartlepool, Heysham in Lancashire, Hinkley Point in Somerset, Oldbury in South Gloucestershire, Sellafield in Cumbria, Sizewell in Suffolk and Wylfa on the Isle of Anglesey. All are at existing nuclear sites.
Announcing the deal with French president Nicolas Sarkozy, British Prime Minister David Cameron said “Today, we match that ambition [of an earlier deal on defence policy] on nuclear energy. As two great civil nuclear nations, we will combine our expertise to strengthen industrial partnership, increase nuclear safety and create jobs at home.”
The Secretary of State for Energy and Climate Change, Edward Davey, emphasised the UK’s commitment to investment in a new generation of nuclear technology. “We need hundreds of billions of pounds of investment in clean energy products in the UK. There are plans for new nuclear in Somerset, Suffolk, Cumbria, North Wales and Gloucestershire.”
This pattern of new building is echoed elsewhere. There are currently over 60 reactors under construction, mainly in Asia but also in the USA and Russia, in 14 countries worldwide, according to the World Nuclear Association. There is also a drive for increased capacity in existing reactors and plans to build over 150 further reactors in countries around the globe.
Thus, far from nuclear power being gradually phased out as a result of disasters such as that experienced at Fukushima, it is going to be an important source of electricity for years to come. Of course, with the potential for failures at nuclear facilities to cause large amounts of damage to plant workers, nearby residents and the local environment, safety is of paramount concern.
A report commissioned by the UK government and authored by chief nuclear inspector Dr Mike Weightman to look into the Fukushima disaster and what changes should be made to UK nuclear policy as a result, reported back on the 11th October 2011. It was generally positive about the safety regime at UK nuclear sites. It was critical, however, of the methods employed at the Fukushima Daiichi plant to assess the risks associated with Tsunamis. “It is understood... that the Tsunami risk is currently addressed using a publication by the Japanese society for Civil Engineers. It does not appear that the approach adopted is a probabilistic one,... rather a series of scenarios are postulated. The rationale for selection of the scenarios is not immediately clear.”
The report contrasts this with the UK’s methods for assessing risks in nuclear facilities. Central to the UK’s risk assessment and reduction regime is Probabilistic Safety Analysis (PSA). One of the Fukushima report’s main conclusions, FR-4, states “The circumstances of the Fukushima accident have heightened the importance of Level 2 Probabilistic Safety Analysis for all nuclear facilities that could have accidents with significant off-site consequences.”
Leaving aside the issue of what level 2 means, this begs the question: what is a Probabilistic Safety Analysis?
Probabilistic Safety Analysis, more commonly known as Probabilistic Risk Analysis (PRA), is a tool used for regulatory decision making and management risk control. It aims to quantify risk, with a particular emphasis on the estimation of the uncertainty inherent in any mathematical modelling of risk. Risk in this setting can be thought of as the collections of scenarios, probabilities and consequences which can arise from a specific activity. A more common definition in the UK is that a risk is the chance that something or someone valued is adversely affected by a hazard, where hazard is defined as potential for harm. A PRA utilises a wide range of modelling tools including fault and event trees, dependent failure models, reliability database modelling and expert elicitation methods to assess, and quantify, risks.
In order to aid understanding of current PRA techniques it will be useful to briefly run through its history. In doing so we follow the timeline set out in Bedford and Cooke (2001). Although the first attempt at modelling risk in a systematic manner was undertaken as part of NASA’s aerospace program, it was in the nuclear sector that PRA really took off (no pun intended). In fact, it was it was in the USA that the first risk assessment which could realistically be called a PRA took place. This was the Reactor Safety Study published by the American Nuclear Regulatory Commission in 1975. This was far from universally accepted initially, however. Members of the American Physical Society described it as “fairly unsatisfactory” and the Lewis Report of 1979, commissioned by the US Congress, identified sufficient flaws in the methodologies used to evaluate probabilities, in spite of a generally positive attitude towards the aims of the procedure, that the future of the PRA was in doubt.
This all changed, however, with the Three Mile Island nuclear accident, also in 1979, which provided apparent validation of the Reactor Safety Study. The accident pathway, which caused the melting of part of the core of the TMI-2 reactor, was identified as a loss of coolant in the reactor. The risk of an event of this accident type had been identified as one of the more likely in the Reactor Safety Study. In the years immediately following this PRA became far more common but with many of the weaknesses of the Reactor Safety Study identified in the Lewis Report eliminated. In particular, the degree of belief interpretation of probability began to be introduced.
PRA, as we have seen already in the guise of PSA in the UK, is now an established part of the regulation of the nuclear sector in many nations. In both the UK and the USA a central theme of the regulation in this area is the ALARP (As Low As Reasonably Practicable) principle. In the UK this is overseen by the Health and Safety Executive (HSE). Their guidance on risk reduction focuses heavily on the ALARP principle. The HSE website says that in case of risk management managers are expected to be able to demonstrate “that the risk has been reduced ‘as low as reasonably practicable’ (ALARP); in those situations where the work activity is unusual (i.e. good practice is not yet established) or where there is a risk of a disaster (e.g. petrochemical and nuclear installations).” In the USA this function is served by the Nuclear Regulatory Commission (NRC). A diagram representing ALARP is given in Figure 3.
Figure 3: The ALARP diagram
We see from the diagram that risk is separated into three regions; unacceptable, tolerable and broadly acceptable. The unacceptable and broadly acceptable regions are fairly self-explanatory. Risks in the tolerable region are regarded as acceptable as long as sufficient mitigating action has been taken to reduce them to as low as can be expected (reasonably practicable).
This middle region is therefore the ALARP region. The region represents a balance between improving safety at a nuclear facility and the costs associated with such safety measures. To do so a cost benefit analysis is typically carried out. This requires putting a financial value on a human life. The value of a human life is a difficult thing to quantify, however. It is also likely to vary depending on who you ask and what you ask them. In the UK the figure typically used is one derived by the Department of Transport. Quite a few different approaches have been advocated over the last 30 years based on studies carried out in 1982, 1991, 1995-1996 and 1997. The idea is that the amount chosen should be representative of the value attached by a cross section of the community. It is important in such an exercise, as in any sampling procedure, to be careful about how the questions are posed. Two common types of question asked in such investigations are concerned either with the amount an individual is willing to pay to avoid the risk in question or the amount an individual would accept to become exposed to the risk. Typically people will answer the two questions differently for the same risk, with people specifying a much larger value for the second. The UK takes an approach based on the willingness to pay. The value of a human life in 2009, calculated in this way, was £1,585,510. In the USA the NRC value a human life at $3 million.
Clearly an accident resulting in 100 deaths is worse than an accident which results in 10. But is a single incident which results in 10 deaths the same, in terms of how undesirable it is, as 10 incidents each with 1 fatality? That is, should group risk be considered differently to individual risk over a number of individuals? In the Netherlands it is, with a single incident with a large number of casualties being regarded as worse than the same number of casualties resulting from several smaller incidents. Indeed, it has been written into law. This separates societal risk from individual risk. This is also consistent, of course, with the way in which such events are reported in the media. The UK does not use such a formulation in regulation, however, although it has been used, particularly in the chemical process sector. A number of UK studies have concluded that it is simply the number of fatalities which is important in the judgement of how serious a risk is, and not the severity of the incidents themselves.
Societal risk is typically measured in terms of the frequency of accidents with a specific number, n, of casualties. It is often represented using Fn curves, an example of which is given in Figure 4. These plot the numbers of casualties on the x-axis against the probability of at least that number of deaths on the y-axis, on a logarithmic scale.
Such curves can be used in regulation. This separates the plot in Figure 4 into regions in a similar manner to the ALARP principle. Curves, and indeed portions of curves, can then be classified as “unacceptable” (the upper right region of the plot), “acceptable” (the bottom left region) and “reduction desired” (the middle region). In general, for a risk to be seen as acceptable, the whole of the curve must be in the acceptable region. An example of what such a criterion for risk regulation would look like is given in Figure 5. The UK HSE recommends such criteria have a slope of -1 whereas in other countries other slopes are used. For example in the Netherlands a slope of -2 is preferred. This suggests a stronger aversion than the UK to large incidents.
Figure 4: An example of an Fn curve
Figure 5: An example of risk regulation based on Fn curves
Of course measuring and making decisions to mitigate risk, for facilities as large and complex as a nuclear power plant, is a long and involved task. While the need to follow good engineering practice makes up a large part of risk regulation, the evaluation of the probabilities associated with the adverse consequences of accidents is a useful element of a risk analysis, particularly in regard of decision making. As such Probabilistic Risk Analysis continues to play a role, as it has now for over 40 years, in the safe running of nuclear power plants all over the world. And looks likely to continue to in the future.
My thanks go to Professor Tim Bedford for suggestions which improved the article.
This article was a runner-up in the Young Statisticians Writing Competition. The author, Dr Kevin Wilson, is a Research Associate at the University of Strathclyde. Dr Wilson completed his PhD in Bayesian Statistics in 2011.