**3.3. Do the accident data represent a random sample?**

steadily until the mid-1980s. After that it grew only from 420 to about 450 in 2011. From this

**Table A1** in Appendix shows for all countries worldwide the total amount of nuclear energy produced, of reactor-years and accidents. The total energy in TWh is produced until 31 Dec. 2015. The amount of reactor-years has been calculated from the Wikipedia sources [3, 4] until

First of all one has to define nuclear incidents or accidents. In 1990, the IAEA introduced the INES scale of incidents or accidents with seven levels [5]. The level 1 event is called an anomaly with, e.g. 'minor problems with safety components…', levels 2–4 are called incidents and levels 5–7 are called accidents. Two of the three destroyed reactors in Fukushima and the accident in Chernobyl were classified as level 7 with 'Major release of radioactive material with widespread health and environmental effects…'. The 1979 Three Mile Island accident in

The USA uses a different scale to classify all, not only nuclear accidents. Major accidents are 'defined as incidents that either resulted in the loss of human life or more than US\$50,000 of property damage, the amount the US federal government uses to define major energy acci-

While the reactor data are publicly and easily available, this does not hold for the accident

According to the treaty of the International Atomic Energy Agency (IAEA), every member state has to inform the IAEA about events 'at Level 2 or above', but these data are publicly available only for 12 months. So, information about accidents in the past is not easy to get. We found two sources. One set of data has been published by the UK newspaper *The Guardian* [8], and another set published by Benjamin Sovacool in two papers [7, 9] and in his book *Contesting the Future of Nuclear Power* [10]. *The Guardian* list includes INES levels where known. Sovacool

*The Guardian* lists 24 and Sovacool 99 events related to all kinds of nuclear technology. Both lists include the same core melt accidents: Windscale, UK, 1957, in a production plant for military use; Simi Valley, USA, 1959, in a research reactor; Monroe, USA, 1966, in a demonstration breeder reactor; Dumfries, UK, 1967, in a power reactor; Lucens, Switzerland, 1969, in an experimental reactor; Three Mile Island, USA, 1979, in a power reactor; Chernobyl, USSR, 1986, in a power reactor; and Fukushima, Japan, 2011, in three power reactors on the same site. The accidents in the three Fukushima reactors were caused by the same earthquake and the subsequent tsunami so we count them as one. This leaves four core melt accidents in power reactors. In order to analyse the learning effect, we treated *The Guardian* and Sovacool data separately. From *The Guardian*'s list of 24 incidents, we included only the ones related to power production.

The total operating time of all reactors until the end of 2011 was 14,766 reactor-years.

time the number of reactors remained nearly constant.

140 Statistics - Growing Data Sets and Growing Demand for Statistics

31.12.2011 to be comparable with the accident data.

the USA was level 5 with 'Severe damage to the reactor core…' [6].

lists 'major accidents' according to the USA definition.

**3.2. How many accidents?**

dents that must be reported' [7].

data.

These lists of publicly known events represent a sample of all incidents and accidents. Only random samples allow to draw conclusions to the underlying population. But are these samples really random? The data had been published by nuclear regulating authorities or collected by scientists, journalists and interested laypeople from a multitude of sources. Depending on the duties of the regulators or the public interest in nuclear energy or the emphasis of the press towards it, events might be detected more often in some countries than in others. So, we compared the number of (known) incidents in each country with its reactor-years.

If the incident probability is the same in all countries and if the probability to detect an accident is also independent of the country, then the number of accidents in a country should be proportional to the number of reactor-years in that country. Plotting the number of accidents versus the reactor-years should result in a straight line. A plot of these data is shown in **Figure 1**. The rightmost point shows the USA data.

So, for all countries except the USA, there seems to be a linear dependence between reactoryears and number of accidents. This is supported by a linear regression for all countries except the USA which gives a slope of 0.0036781 accidents per reactor-year with a standard error of 0.0004785. For each country but the USA, the expected value calculated from the 0.0036781 accidents per reactor-year is within the 95% confidence interval of the empirical accidents. Only for the USA, the empirical accident number of 54 in 3731 reactor-years is far away from the expected number of about 15.2.

While the data for all countries except the USA are compatible with a rate of 3.678 accidents per 1000 reactor-years, the USA data resemble 13.06 accidents per 1000 reactor-years.

**Figure 1.** Total number of accidents in several countries versus total number of its reactor-years; the straight line is a linear fit through all data except the rightmost point (data from **Table 1**).

So, with the exception of the USA, there is no indication from the limited available data of non-random sampling or of countries having different overall accident rates. The USA data indicate that here either sampling is not random or the accident rate is higher than in the rest of the world. The present data do not allow us to determine which of these alternatives is the more likely explanation and further studies are needed.

There remain four core melt accidents in nuclear reactors for power generation.

reactor-years. Nevertheless, the most probable value is 1 in 3700 reactor-years.

*p* = \_\_\_\_\_ <sup>4</sup>

0.2 and 1.8 accidents.

**5. Learning effects**

**5.1. Introduction**

a given date.

but the analysis here is more detailed.

So, we expect one severe accident in 3700 reactor-years.

Given the number of severe accidents, 4, and the cumulative reactor-years, 14,766, it is straightforward to calculate the probability *p* of a core melt accident at one reactor in 1 year:

<sup>14766</sup> <sup>=</sup> 2.70 <sup>×</sup> <sup>10</sup>−4 <sup>=</sup> \_\_\_\_ <sup>1</sup>

This simple calculation contains several uncertainties. Firstly, it is assumed that all reactors at all times have the same failure probability. Secondly, because of the small sample size of four events, it is subject to statistical fluctuations. This can be expressed through the confidence interval. Within a 95% confidence limit, the empirical value of four events leads to a confidence interval of 1.0899 and 10.2416 events in 14,766 reactor-years. Therefore, with a confidence of 95%, the failure rate is between one accident in 1442 and one accident in 13,548

Based on this value, it is possible to calculate the probability of accidents in the future. In a world with 443 reactors, we should expect 2.99 core melt accidents within the next 25 years with a 95% confidence interval of 0.82 accidents and 7.7 accidents. The USA with 104 reactors have to expect 0.7 core melt accidents within 25 years, with 95% confidence interval between

Experience and learning from operating power reactors and from analysing incidents and accidents are important for further reducing accident rates. Increasing operational experience should result in decreasing accident rates. This can be tested empirically by comparing accident rates with the amount of operational experience. In a simple approach, operational experience can be measured by the cumulative number of reactor-years up to

The small number of core melt accidents makes it difficult to detect any learning effect. Therefore, for this analysis we also included minor accidents and incidents. The two different datasets from *The Guardian* with 35 accidents and from Sovacool with 99 accidents were analysed independently. *The Guardian* data were grouped according to INES levels, and here all incidents of level 2 and above were included. One of the criteria for a level 2 incident is a 'significant contamination within a facility into an area not expected by design'. So, these incidents must be avoided by all means. From Sovacool's data all accidents related to nuclear power generation were included. Some of the basic results given below are summarised in [1],

<sup>3700</sup> (2)

Severe Nuclear Accidents and Learning Effects http://dx.doi.org/10.5772/intechopen.76637 143
