**3. Data acquisition**

prior to accidents by analysing possible paths towards a severe accident, rather than using

After an accident very often 'learning from experience' is claimed. The luckily low number of severe accidents does not allow for testing this claim. But reactor operators should be interested in reducing all incidents and accidents; so, their frequency should decrease with increasing operating experience. We use the total time reactors are operating, the reactor-years, as a measure of experience, analyse the accidents as a function of this experience with generalised

Accidents can and did happen in several areas of nuclear energy, e.g. military use for weapons or submarine propulsion, medical use or fundamental research. Discussing the risks of nuclear energy involves very different arguments in all these areas. We restricted the study to

According to our analysis, we have to expect one core melt accident in 3700 reactor-years with a 95% confidence interval of one in 1442 reactor-years and one in 13,548 reactor-years. In a world with 443 reactors, with 95% confidence we have to expect between 0.82 and 7.7 core

Analysing all known accidents, we can show a learning effect. The probability of an incident or accident per reactor-year decreased from 0.01 in 1963 to 0.004 in 2010. Furthermore, there

It is well known that the actual number of all incidents and accidents is much higher than the numbers published in scientific journals. Therefore, we studied whether the known incidents and accidents are distributed randomly over the reactors using countries. While the data are random for most of the countries, this is not the case for the USA. From the present data, we cannot decide whether this is due to higher incident rates or to more effective sampling.

After this introduction the second section will explain some basics of the Poisson distribution. In Section 3 we present the data acquisition and its problems. Section 4 contains the discussion of core melt accidents and predictions for future events. The learning effect analysis is

While some of the results have been published already elsewhere [1], the underlying statisti-

Rare and random incidents related to a time of reference, an area of reference or similar can be described by the Poisson distribution. Examples are the number of surface defects in body part stamping in the automotive industry or the number of calls in a call centre within a given time. If the probability of an incident per time is known to be *p*, then within the time interval *T*, we expect a total number of *λ* = *pT* incidents. But the actual number of incidents within *T* will

existing data to determine probability empirically.

138 Statistics - Growing Data Sets and Growing Demand for Statistics

accidents in nuclear reactors for power generation.

melt accidents within the next 25 years.

presented in Section 5.

cal work is presented here.

**2. Poisson distribution**

linear models and compare a frequentist and a Bayesian approach.

is an indication of a slightly larger learning effect prior to 1963.

### **3.1. How many reactors?**

The International Atomic Energy Agency in Vienna publishes data on all power reactors worldwide [2]. The same and additional information about connection to the grid, shut down, operator, manufacturer and fuel supplier can be found in several Wikipedia entries [3, 4].

It was 1952 when the Soviet Union connected the first nuclear power reactor worldwide to the grid. Two years later the UK followed with Calder Hall. The number of reactors increased steadily until the mid-1980s. After that it grew only from 420 to about 450 in 2011. From this time the number of reactors remained nearly constant.

This left 16 accidents of INES level 2 and higher. From Sovacool's list, we excluded five acci-

Severe Nuclear Accidents and Learning Effects http://dx.doi.org/10.5772/intechopen.76637 141

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

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

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

While the data for all countries except the USA are compatible with a rate of 3.678 accidents

**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**).

per 1000 reactor-years, the USA data resemble 13.06 accidents per 1000 reactor-years.

dents not related to power generation.

rightmost point shows the USA data.

the expected number of about 15.2.

reactor-years.

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

**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 31.12.2011 to be comparable with the accident data.

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

### **3.2. How many accidents?**

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

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 accidents that must be reported' [7].

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

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 lists 'major accidents' according to the USA definition.

*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. This left 16 accidents of INES level 2 and higher. From Sovacool's list, we excluded five accidents not related to power generation.
