A novel stratified sampler with unbalanced refinement for network reliability assessment

We investigate stratified sampling in the context of network reliability assessment. We propose an unbalanced stratum refinement procedure, which operates on a partition of network components into clusters and the number of failed components within each cluster. The size of each refined stratum and the associated conditional failure probability, collectively termed failure signatures, can be calculated and estimated using the conditional Bernoulli model. The estimator is further improved by determining the minimum number of component failure $i^*$ to reach system failure and then by considering only strata with at least $i^*$ failed components. We propose a heuristic but practicable approximation of the optimal sample size for all strata, assuming a coherent network performance function. The efficiency of the proposed stratified sampler with unbalanced refinement (SSuR) is demonstrated through two network reliability problems.