After the Fukushima disaster, the authors analyzed all past coremelt accidents and estimated a failure rate of 1 per 3704 reactor years. This rate indicates that more than one such accident could occur somewhere in the world within the next decade. The authors also analyzed the role that learning from past accidents can play over time. This analysis showed few or no learning effects occurring, depending on the database used. Because the International Atomic Energy Agency (IAEA) has no publicly available list of nuclear accidents, the authors used data compiled by the Guardian newspaper and the energy researcher Benjamin Sovacool. The results suggest that there are likely to be more severe nuclear accidents than have been expected and support Charles Perrow’s “normal accidents” theory that nuclear power reactors cannot be operated without major accidents. However, a more detailed analysis of nuclear accident probabilities needs more transparency from the IAEA. Public support for nuclear power cannot currently be based on full knowledge simply because important information is not available.
In his essay, “A skeptic’s view of nuclear energy,” Princeton University nuclear expert Harold A. Feiveson writes that he is not antinuclear, and he lauds improvements in the operation and reliability of nuclear power plants in recent years as “striking.” However, he notes, “Even if the chance of a severe accident were, say, one in a million per reactor year, a future nuclear capacity of 1,000 reactors worldwide would be faced with a 1 percent chance of such an accident each 10year period – low perhaps, but not negligible considering the consequences” (Feiveson
2009, 65).
The 2011 Fukushima disaster in Japan suggested once more that severe nuclear accidents could be even more frequent than safety studies had predicted and Feiveson had hoped. So we decided to estimate the probability of a severe accident – that is, a coremelt accident – by relating the number of past coremelt accidents to the total number of years reactors have been operating (i.e. “reactor years”).
This type of prediction often runs up against the argument that nuclear operators learn from the past. Therefore we also tried to account for any learning effects in our analysis. We restricted our analysis to accidents related to civil nuclear reactors used for power generation, as arguments about tradeoffs for using nuclear technology differ depending on the application. And, because the International Atomic Energy Agency (IAEA) does not distribute comprehensive, longterm reports on nuclear incidents and accidents because of confidentiality agreements with the countries it works with, we have had to use alternative sources for information on nuclear accidents over time.
By our calculations, the overall probability of a coremelt accident in the next decade, in a world with 443 reactors, is almost 70%. (Because of statistical uncertainty, however, the probability could range from about 28% to roughly 95%.) The United States, with 104 reactors, has about a 50% probability of experiencing one coremelt accident within the next 25 years.
^{1}
In 1954 the Soviet Union connected the first nuclear power reactor to the grid; Calder Hall in England followed 2 years later. The number of reactors in the world then increased steadily until the mid1980s. From then until 2011, the number grew only from about 420 to nearly 450. A more precise calculation takes into account data from the IAEA (
2006, 46–51, 81), given until 2005, assuming the number did not change significantly after 2005. Thus we estimate that there were 14,816 cumulative reactor years from 1954 until March 2011.
Since 1990, the IAEA has used a sevenlevel International Nuclear Event Scale (INES) to measure the severity of nuclear incidents and accidents (IAEA
2008). Two of the three reactor accidents at Fukushima rank at Level 7, as does Chernobyl. According to the IAEA treaty, “countries are strongly encouraged” to report any events “at Level 2 or above” or “events attracting international public interest” (IAEA
2009, 10). It is not possible to assign INES levels to all accidents prior to 1990.
In the literature there are slightly different definitions of a minor, major, or severe accident. We use as the indicator for a severe nuclear accident the melting of nuclear fuel within the reactor. These coremelt accidents are the ones we analyze further.
One further hurdle came from the IAEA itself. Despite its encouragement of countries to report nuclear accidents, the agency makes INES information public for only 1 year after publication. Thus while the number of reactors connected to the grid is well known (IAEA
2006, 81), information on accidents at nuclear sites is hard to get. We tried several times to acquire better data from the IAEA without success.
^{2} As Rejane Spiegelberg Planer, a senior safety officer with the agency and an INES coordinator, informed one of the authors in an email on 1 April 2011, “There is no publicly available list of events rated using INES.” We therefore collected our data from two publicly available lists of nuclear accidents, one published by the
Guardiannewspaper (Rogers
2011), the other in two papers by Benjamin K. Sovacool (
2008,
2010) and in his book
Contesting the Future of Nuclear Power (
2011). The
Guardian list contains 35 incidents and accidents, whereas Sovacool lists 99 major accidents.
Both the
Guardian and Sovacool lists include the same eight coremelt accidents since 1952:

Windscale, England, 1957: A fire ignites plutonium piles

Simi Valley, California, 1959: A partial core melt takes place at the Santa Susana Field Laboratory’s Sodium Reactor Experiment

Monroe, Michigan, 1966: The sodium cooling system of a demonstration breeder reactor causes partial core melt

Dumfries, Scotland, 1967: Fuel rods catch fire and cause a partial core melt

Lucens, Switzerland, 1969: The coolant system of an experimental reactor malfunctions

Pennsylvania, 1979: Three Mile Island

Soviet Union, 1986: Chernobyl

Japan, 2011: Fukushima
We excluded from our analysis the Windscale military reactor accident in 1957 and three research reactor accidents (Simi Valley in 1959, Monroe in 1966, and Lucens in 1969). Finally, we counted the damage of three reactors in Fukushima as one accident because they were triggered by the same cause, a tsunami. This leaves four accidents with core melts in civil reactors for power generation.
Using simple statistics, the probability of a coremelt accident within 1 year of reactor operation is 4 in 14,816 reactor years, or 1 in 3704 reactor years. But this simplistic analysis is subject to a large degree of uncertainty. First, it assumes the absence of any learning effect, and that reactors in all countries have the same failure probability. Second, the estimated failure probability is subject to statistical error: One can conclude with only 95% confidence that the true failure probability for a coremelt accident is between 1 in 14,300 reactor years and 1 in 1450 reactor years. Thus the best estimate is 1 in 3704 reactor years.
Having established this, we can calculate the probability of at least one core melt for a given number of calendar years. Within the next 10 years, the probability of a coremelt accident in a world with 443 reactors is 69.8%. Because of the statistical uncertainty mentioned above, this value could range from 27.8% to 95.3%. The United States, with 104 reactors, can therefore expect one accident within the next 25 years with a probability of 50.4%.
Did the reactor operators learn?
We also wanted to see whether accidents become less frequent with more operational experience. But simply analyzing the number of severe accidents against reactor years is not very illuminating because, luckily, these accidents are rather rare. So we examined the relationship between the cumulative number of all accidents, from severe to minor ones, and cumulative reactor years. The accident rate is then estimated as the ratio of cumulative number of accidents to cumulative reactor years. If the probability of an accident remained constant over time, then a graph of the above accidentrate estimates against reactor years would exhibit no trend, whereas a learning effect would result in a decreasing accident probability and the graph would exhibit a decreasing trend.
We began by plotting the data from the
Guardian list, with a few exclusions.
^{3} The graph shows a high accident rate at the beginning because of one accident in Russia in 1957. The accident rate then drops because the following years were accidentfree. After around 500 reactor years, the plot appears to stabilize, varying around a constant value. This is confirmed by a detailed statistical analysis, which produces a probability for a (minor or major) accident in a nuclear power plant of about 1 in 1000 reactor years and shows no evidence of a learning effect.
An analysis of Sovacool’s more extensive data, however, promises more insight. Sovacool does not list his data according to INES levels and instead uses a different definition of a major accident: One that causes human deaths or more than $50,000 in damage, the same amount used by the US government to indicate a major accident (Sovacool
2010, 380).
^{4} When plotted, Sovacool’s data shows an initial period with strong learning effects, followed by a remaining period with much weaker or even absent learning effect.
Using a generalized regression analysis, we further found some evidence of a fairly consistent rate of learning in the period from around 1962 to 2011, although the evidence to rule out “no learning effect” completely is weak. The data indicate a stronger learning effect in the first years of the nuclear age, but this effect is not significantly different from the later learning effect. If the initial and final learning rates did differ, then the estimated year when the learning rate changed would be 1961; but the data would also be consistent with a change year between 1957 and 1965.
Nevertheless, from 1962 to 2010 the probability of a minor or severe accident at a reactor decreased by a factor of 2.5 (from 10 accidents per 100 reactor years to 4 accidents per 100 reactor years), while the operational experience increased by a factor of 170.
Unfortunately, the most important ingredient for a reliable analysis of this kind would be comprehensive timeseries data, which are filed at the IAEA but not available for the public. While we could only use Sovacool’s list with 94 events worldwide, Phillip Greenberg writes that “between 1990 and 1992 the US Nuclear Regulatory Commission received more than 6600 ‘Licensee Event Reports’ because US nuclear plants failed to operate as designed and 107 reports because of significant events (including safety system malfunctions and unplanned and immediate reactor shutdowns)” (Greenberg
1996, 130–131).
Furthermore, based on our regression analysis we calculated the expected numbers of accidents in each year and compared these with the actual numbers of accidents. The differences between these two sets of figures were consistent with what one would expect if all reactors had the same failure probability. If the reactors had different failure probabilities, then this would induce additional variation between the observed and expected numbers of accidents. Thus there is no indication that some reactors are less prone to failure than others.
Normal accidents and the need for more data
In his classic book
Normal Accidents, Charles Perrow developed the theory that systems with tight coupling of, and complex interaction between, components and subsystems are inherently unsafe. He attributes nuclear power plants with the highest complexity and tightest coupling, in both aspects ranked above space missions or nuclear weapon accidents (Perrow
1999, 327). And Scott Sagan adds: “…what I will call ‘normal accident theory,’ presents a much more pessimistic prediction: Serious accidents with complex high technologies are inevitable” (Sagan
1995, 13). Statistical analysis supports this unsettling probability.
In conclusion, the number of coremelt accidents that can be expected over time in nuclear power stations is larger than previously expected. To assess the risk of similar events occurring in the future, it is necessary to determine whether nuclear power operators learn from their experiences. Our work shows that it is possible to investigate such learning effects through statistical analysis. Until the IAEA makes the relevant data available, however, the full story of accident probability and learning effects will remain untold.
No potential conflict of interest was reported by the authors.
^{1.} In the past, several studies have investigated the probability of a core melt using the probabilistic risk assessment (PRA) method. This determines probability prior to accidents by analyzing possible paths toward a severe accident, rather than using existing data to determine probability empirically. Two studies by the US Nuclear Regulatory Commission (
1975,
1990) as well as a German government study (Hörtner
1980) examined seven different cases or reactors. Three calculations resulted in 1 accident in more than 200,000 reactor years, and a further three resulted in 1 accident in 11,000–25,000 reactor years. Only the result for the Zion reactor had an accident rate similar to ours, with 1 accident in 3000 years. After Chernobyl, Islam and Lindgren (
1986, 691) published a short note in
Nature in which, based on the known accidents (Three Mile Island and Chernobyl) and reactor years (approximately 4000) at the time, they concluded that “…the probability of having one accident every two decades is more than 95%.” Regarding PRA, they wrote: “Our view is that this method should be replaced by risk assessment using the observed data.” This sparked an intensive discussion of statistical issues in the following year (Edwards
1986; Schwartz
1986; Fröhner
1987; Chow and Oliver
1987; Edwards
1987); however, there was agreement on the substantive conclusions of Islam and Lindgren.
^{2.} An October 5 2011 email by an IAEA official to one of the authors read: “Please note that old NEWS reports are not made available by the IAEA Secretariat. This is so because the reports have been provided by participating INES countries under the condition that the reports be only publicly available on NEWS for a period of 12 months (formerly 6 months). This condition has been agreed among the participating countries to prevent inappropriate use of the information (such as trying to use the information as a basis for statistical analyses and comparisons of safety performance of participating countries…”.
^{3.} We excluded three accidents, namely Ikitelli in 1999, Yanangio in 1999, and Fleurus in 2006, because they were related to medical use. We also excluded the 1952 research reactor accident in Chalk River, Ontario. That left 16 accidents of Level 2 or higher.
^{4.} From Sovacool’s list of 99 nuclear accidents, we excluded five: Chalk River in 1952, Windscale in 1957, Simi Valley in 1959, Monroe in 1966, and Lucens in 1969.
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