Algorithm computes failure signatures and repair policies for complex systems
Per-State Signatures and Mean Time-to-Failure: An Algorithm for Systems With Simultaneous Failures
Data Structures and Algorithms
Summary
Many systems break down over time, and understanding which parts fail and when helps fix them better. The authors created an algorithm that studies every possible state of a system to predict how long it will last and to find the best ways to repair it. Their approach works even when many parts fail at once, which was hard before. They tested their method on many example systems and found it helps choose near-optimal repair plans.
What this means in practice
- •For maintenance engineers: Determine when and how to repair complex equipment by evaluating detailed failure probabilities and expected lifetimes for all conditions of system components.
- •For network reliability teams: Select optimal repair thresholds in communication networks where multiple link failures can happen simultaneously, improving uptime based on accurate failure state analysis.
Authors
Guido Lagos, Simón Ávila
Abstract
We present an algorithm that computes the structural signature and the mean time-to-failure (MTTF) of a monotone binary system at every one of its states, rather than only at the state in which all components work. It makes no assumption on the structure function and evaluates it exactly once per state, as many times as needed for the signature of the complete system alone, so computing the MTTF everywhere costs only a factor polynomial in the number of components over computing it once. As a by-product, it identifies all minimal path sets. We assume exchangeable component failure times whose survivor count is a continuous-time Markov chain. This setting admits simultaneous failures, as in the Lévy-frailty Marshall-Olkin, binomial failure rate and lethal-shock models, where the simplifications available for single failures do not apply. We use the per-state MTTF to define threshold repair policies. We show that the per-state signature is a strictly finer decision criterion than the MTTF: signature dominance at a common failure count implies MTTF dominance, but not conversely. Under the Lévy-frailty Marshall-Olkin model the MTTF is monotone in the state, which yields the long-run cost rate of every threshold policy in a single pass. Experiments on 22 benchmark networks with up to 30 components and 31 failure models show that the best MTTF-threshold policy has a median excess cost of 0.36% over the optimal state-based policy, and that it is never worse than the best policy that repairs after a fixed number of failures.