Measuring and Optimizing System Reliability: A Stochastic Programming Approach

TL;DR

This paper introduces a stochastic programming framework to measure and optimize the reliability of complex systems modeled as graphs, accounting for random component failures and system constraints.

Contribution

It presents a novel computational approach that combines graph modeling, stochastic mixed-integer programming, and continuous approximations to enhance system reliability analysis and design.

Findings

Reliability can be computed via stochastic mixed-integer programming.

The framework accounts for various failure distributions and system constraints.

A scalable continuous approximation method improves computational efficiency.

Abstract

We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges). Under this setting, reliability is defined as the probability of finding a path between sources and sink nodes under random component failures and we show that this measure can be computed by solving a stochastic mixed-integer program. The stochastic programming setting allows us to account for system constraints and general probability distributions to characterize failures and allows us to derive optimization formulations that identify designs of maximum reliability. We also propose a strategy to approximately solve these problems in a scalable manner by using purely continuous formulations.