Verification of rod safety via confidence intervals for a binomial proportion

The probabilistic safety assessed to a set of N fuel rods assembled in one core of a nuclear power reactor is commonly modelled by ∑i≤NXi, where X1, …, XN are independent Bernoulli random variables (rv) with individual probability pi = P (Xi = 1) that the ith rod shows no failure during one cycle. This is the probability of the event that the ith rod will not exceed the failure limit during one cycle. The safety standard presently set by the German Reaktor-Sicherheitskommission (Reactor Safety Commission) requires that the expected number of unfailed rods in the core during one cycle is at least N − 1, i.e., E(∑i≤NXi) = ∑i≤Npi ≥ N − 1, whereby a confidence level of 0.95 for the verification of this condition is demanded. In this paper, we provide an approach, based on the Clopper–Pearson confidence interval for the proportion p of a binomial B(n, p) distribution, how to verify this condition with a confidence level of at least 0.95. We extend our approach to the case, where the set of N fuel rods is arranged in strata, possibly due to different design in each stratum.