Monte Carlo simulation for the optimization of maintenance strategies in degrading systems

Abstract

Effective maintenance strategies that balance system performance and robustness are crucial for both public and private enterprises. In response to increasing competition and the high cost of infrastructure and equipment, decision-makers are increasingly relying on mathematical modeling to support optimization and resilience. This paper introduces an adaptation criterion for selecting the optimal maintenance policy by simultaneously evaluating performance and robustness, replacing the conventional cost-based model with a Robust Quantification Model (RQM). Our proposed economic criterion is a linear combination of three key elements: the asymptotic average maintenance cost per unit of time (C∞), the standard deviation (σ) of the maintenance cost per replacement cycle (MCPRC), which measures the variability of total maintenance costs over each renewal cycle, and the weight parameter (λ) reflecting the trade-off between cost performance and robustness. This combined criterion allows for a joint assessment of stability and economic efficiency. We evaluate the three techniques (Block Replacement strategy (BR), Periodic Inspection Replacement strategy (PIR) and Quantile-based Inspection Replacement strategy (QIR)) using the proposed robust economic criterion, and compare their effectiveness under uncertain system degradation modeled using a homogeneous Gamma process. Monte Carlo simulations are employed to estimate the expected cost and variability across multiple degradation scenarios, ensuring empirical accuracy of the proposed criterion. The simulation results demonstrate that the proposed criterion effectively captures both the average cost behavior and its variability, providing a comprehensive tool for selecting resilient and cost-effective maintenance strategies in degrading systems.

Topics & Concepts