A novel stratified sampler with unbalanced refinement for network reliability assessment

TL;DR

This paper introduces a new stratified sampling method with unbalanced refinement for more efficient network reliability assessment, improving estimation accuracy by focusing on critical failure signatures.

Contribution

It proposes an unbalanced stratum refinement procedure and a heuristic for optimal sample size, enhancing network reliability estimation efficiency.

Findings

Demonstrated improved efficiency on two network reliability problems.

Effectively estimates failure signatures using conditional Bernoulli model.

Reduces variance by focusing sampling on critical failure strata.

Abstract

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.