A novel stratified sampler with unbalanced refinement for network reliability assessment

2025-06-01

AI Summary

To address the low efficiency and poor robustness of conventional stratified sampling in network reliability assessment, this paper proposes an imbalanced stratified sampling method. It jointly stratifies based on component clustering and system failure count, employs a conditional Bernoulli model to estimate failure signatures per stratum, and—novelly—couples stratification refinement with the system-level critical failure number $i^*$ to enable threshold-driven pruning of ineffective strata. Furthermore, a heuristic optimal sample allocation strategy is designed specifically for connectivity-based performance functions. Experimental results on two canonical network reliability problems demonstrate that the proposed method significantly outperforms traditional stratified sampling and importance sampling in both accuracy and efficiency: variance reduction exceeds 40%, while robustness and scalability are markedly improved.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• Assessing network reliability via stratified sampling
• Optimizing unbalanced stratum refinement for failure signatures
• Improving estimator efficiency using conditional Bernoulli model

Innovation

• Unbalanced stratum refinement for network clusters
• Conditional Bernoulli model for failure signatures
• Heuristic optimal sample size approximation