HYBRID MARKOV–MONTE CARLO RAM MODELLING FOR MULTI‑STATE ASSETS WITH NON‑EXPONENTIAL FAILURE/REPAIR DISTRIBUTION

Abstract

Reliability, Availability, and Maintainability (RAM) modelling is fundamental to asset-intensive industries. Traditional RAM techniques, particularly continuous-time Markov chains (CTMC), assume exponential distributions for failure and repair times, which rarely hold in real-world systems where Weibull, lognormal, or gamma behaviors dominate. This paper presents a hybrid Markov–Monte Carlo (HM-MC) framework for RAM assessment of multi-state assets operating under non-exponential failure and repair distributions. The proposed method combines the state-transition structure of Markov models with Monte Carlo simulation to sample sojourn times from arbitrary distributions while preserving state memory. Using a three-state industrial pump system (healthy, degraded, failed) as a test asset, we compare the HM-MC method against traditional CTMC and pure Monte Carlo over 10,000 simulated operating hours. Results demonstrate that CTMC overestimates availability by 18.3% (0.94 vs 0.79 actual) when actual failure times follow Weibull(β=1.5). The HM-MC method achieves availability estimates within 2.1% error of ground truth while reducing computational variance by 62% compared to pure Monte Carlo. The framework offers a practical pathway for accurate RAM modelling without mathematical intractability.