  We propose a modification of the improved cross entropy (iCE) method to
enhance its performance for network reliability assessment. The iCE method
performs a transition from the nominal density to the optimal importance
sampling (IS) density via a parametric distribution model whose cross entropy
with the optimal IS is minimized. The efficiency and accuracy of the iCE method
are largely influenced by the choice of the parametric model. In the context of
reliability of systems with independent multi-state components, the obvious
choice of the parametric family is the categorical distribution. When updating
this distribution model with standard iCE, the probability assigned to a
certain category often converges to 0 due to lack of occurrence of samples from
this category during the adaptive sampling process, resulting in a poor IS
estima tor with a strong negative bias. To circumvent this issue, we propose an
algorithm termed Bayesian improved cross entropy method (BiCE). Thereby, the
posterior predictive distribution is employed to update the parametric model
instead of the weighted maximum likelihood estimation approach employed in the
original iCE method. A set of numerical examples illustrate the efficiency and
accuracy of the proposed method.
