Estimation of Nuclear Power Plant Train Unavailability Using Nonparametric Bootstrap

The distribution of nuclear power plant train (combination of hardware to perform a specific function) unavailability can be very right skewed and contain many zeros, making it difficult to determine an appropriate parametric form. NUREG/CR-6928 and its periodic updates applied a curve fitting approach with various distribution types, including the beta and normal distributions, which has been applied to estimate the nuclear industry-level train unavailability in recent history. However, there have been challenges associated with this approach, for example, the actual data sets often do not follow a beta distribution, while the fit with a normal distribution could generate a negative lower bound for average unavailability. In this paper, we propose a nonparametric bootstrap to estimate the uncertainty for mean train-level unavailability. Applying the nonparametric bootstrap to these data results in an approximate sampling distribution of mean unavailability from which approximate confidence intervals, standard errors, and other statistics can be obtained. The bootstrap distribution can then be fitted to a beta distribution via method of moments to obtain a parametric distribution describing the uncertainty in mean train-specific unavailability. This approach was applied to several real data sets and yielded well behaved sampling distributions of mean unavailability, positive estimates of lower bounds on the mean, and was well approximated with a beta distribution.