Safety Assessment of Fuel Rods via Generalized Bernoulli Chains

The probabilistic safety assessed to N fuel rods assembled in one core of a nuclear reactor is commonly modelled by the sum of N independent Bernoulli random variables, i.e. 1 or 0, with individual safety probability p_i that the i-th rod shows no failure during one cycle, coded by 1. The requirement set by the German Reaktor-Sicherheitskommission (Reactor Safety Commission) demands that the expected number of unfailed rods in the core within one cycle is at least N-1, whereby a confidence level of 0.95 for the verification of this condition is demanded. There is an ongoing debate that this requirement based on an expected value might be a misleading probabilistic safety measure as it does not take into account the accumulated safety probabilities that at least x fuel rods show no failure during one cycle. In this paper we establish a bound for the accumulated safety probability under this safety condition, which implies that with probability greater than 0.98 at least N-3 fuel rods show no failure during one cycle