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

### Harry Martz (TSA-1)

### 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.