On the solution approach for Bayesian modeling of initiating event frequencies and failure rates

Then is a need for plant-specific distributions of incidence and failure rates rather than distributions from pooled data which are based on the ''common incidence rate'' assumption. The so-called superpopulation model satisfies this need through a practically appealing approach that accounts for the variability over the population of plants. Unfortunately, the chosen order in which the integrals with respect to the individual plant rates lambda(i) (i = 0, 1..., m) and the parameters alpha,beta of the Gamma-population distribution are solved seems to drive the solution close to the common incidence rate distribution. It is shown that the solution obtained from interchanging the order and solving the integrals with respect to the individual plant rates by Monte Carlo simulation very quickly provides the plant specific distribution. This differing solution behaviour may be due to the lack of uniform convergence over (alpha,beta, lambda(i) (i = 1,..., m))-space. Examples illustrate the difference that may be observed.