## Bayesian Estimation of Trends in the Scram Rate at Nuclear Power Plants

### Abstract

Reactor scrams can result from initiating events that range from relatively minor incidents to events that are precursors of accidents. The rate at which unplanned scrams occur is thus an important indicator of overall plant performance and reliability. We consider trends in the scram rate at 66 US commercial nuclear power plants based on annual observed scram data from 1984-1993. For an assumed Poisson distribution on the number of unplanned scrams, a gamma prior, and a 'noninformative' hyperprior, a parametric empirical Bayes (PEB) approximation to a full hierarchical Bayes formulation is used to estimate the scram rate for each plant for each year. The PEB-estimated prior and posterior distributions are then subsequently smoothed over time using an exponentially weighted moving average (EWMA). The results indicate that such bi-directional smoothing is quite useful for identifying reliability trends over time.