Abstract
{ "background": "Process-control systems in critical national infrastructure are increasingly complex and vulnerable. Traditional diagnostic methods often fail to adequately quantify and propagate uncertainty in system performance, leading to suboptimal maintenance and risk management strategies.", "purpose and objectives": "This research aimed to develop and evaluate a novel Bayesian hierarchical modelling framework to improve diagnostic accuracy and quantify risk reduction for industrial process-control systems. The objective was to provide a robust probabilistic tool for engineers to prioritise maintenance interventions.", "methodology": "A Bayesian hierarchical model was formulated, integrating diagnostic test data with expert prior knowledge on component failure rates. The core model structure is $y{ij} \\sim \\text{Bernoulli}(\\theta{ij}), \\; \\text{logit}(\\theta{ij}) = \\alphai + \\beta X{ij}$, where $\\alphai \\sim \\text{Normal}(\\mu, \\sigma^2)$ represents plant-specific random effects. Inference was performed using Hamiltonian Monte Carlo sampling, with posterior credible intervals used for all risk estimates.", "findings": "Application to diagnostic data from three mineral processing plants demonstrated a quantifiable reduction in diagnostic uncertainty. The 95% posterior credible interval for mean system failure risk narrowed by approximately 34% compared to conventional frequentist methods, allowing for more precise identification of high-priority components.", "conclusion": "The proposed model provides a statistically rigorous framework for risk assessment that formally incorporates both data and engineering judgement. It represents a significant methodological advance over deterministic or simple probabilistic models currently in use.", "recommendations": "Adoption of this Bayesian hierarchical approach is recommended for asset management in sectors reliant on complex process-control systems. Further work should focus on developing user-friendly software interfaces to facilitate implementation by practising engineers.", "key words": "Bayesian inference, risk assessment, predictive maintenance, industrial diagnostics, probabilistic modelling", "contribution statement": "This paper presents a novel Bayesian hierarchical model that uniquely integrates multi-plant operational data with expert elicitation to reduce uncertainty in process-control system