**4. Statistics of severe nuclear accidents**

### **4.1. Results of previous PRA calculations**

There have been several studies on reactor safety in the past. The first was the reactor safety study or Rasmussen report published in 1975 by the US Nuclear Regulatory Commission as report WASH-1400 or NUREG75/014 [11]. Five years later the German reactors were analysed in the Deutsche Risikostudie Kernkraftwerke [12]. In 1990 *Severe Accident Risks: An Assessment for Five U.S. Nuclear Power Plants* [13] was published. While the first two studies analysed typical reactors in their respective countries, the last one investigated five specified reactors.

What are the results of these studies? WASH-1400 states:

'The Reactor Safety Study carefully examined the various paths leading to core melt. Using methods developed in recent years for estimating the likelihood of such accidents, a probability of occurrence was determined for each core melt accident identified. These probabilities were combined to obtain the total probability of melting the core. The value obtained was about one in 20,000 per reactor per year. With 100 reactors operating, as is anticipated for the U.S. by about 1980, this means that the chance for one such accident is one in 200 per year' [11].

So, the probability for a core melt accident per reactor year is 5 × 10<sup>−</sup><sup>5</sup> .

The results of NUREG 1150 [14] can be found in Tables 3.2, 4.2, 5.2, 6.2 and 7.2 for the reactors Surry, Peach Bottom, Sequoyah, Grand Gulf and Zion, respectively. The German data are in the Deutsche Risikostudie [12]. The mean values vary between 4 × 10<sup>−</sup><sup>6</sup> and 3.40 × 10−4 accidents per reactor-year.

### **4.2. Empirical analysis**

Based on the list and information of Sovacool, the following accidents are not included in the present study of severe accidents: Chalk River (1952) showed no core meltdown; Windscale (1957) was a military reactor only used for weapon production; Simi Valley (1959) was an experimental reactor; Monroe (1966) was an experimental reactor; and Lucens (1969) was an experimental reactor and probably showed no core meltdown. In Fukushima three of the six reactors at the site suffered severe destruction with INES ratings of 5–7. This threefold accident is counted as one because all three were triggered by the same cause, the tsunami with subsequent earthquake.

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

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:

$$p = \frac{4}{14766} = 2.70 \times 10^{-4} = \frac{1}{3700} \tag{2}$$

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

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

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 0.2 and 1.8 accidents.
