Abstract
{ "background": "Process-control systems are critical for industrial and infrastructure operations, yet their reliability in developing contexts is poorly quantified. Traditional reliability models often fail to account for site-specific operational variances and data scarcity, which are common challenges in many African industrial settings.", "purpose and objectives": "This study aimed to develop and validate a Bayesian hierarchical modelling framework to assess the reliability of process-control systems, explicitly addressing data limitations and heterogeneous operational conditions. The objective was to provide a robust, adaptable tool for engineers to quantify failure risks and inform maintenance strategies.", "methodology": "A Bayesian hierarchical model was constructed, integrating field failure data from multiple control systems across different industrial sites. The core reliability parameter, the failure rate $\lambdai$, for system $i$ was modelled as $\lambdai \\sim \\text{Gamma}(\\alpha, \\beta)$, with hyperpriors on $\\alpha$ and $\\beta$ to pool information across sites. Posterior distributions were estimated using Markov Chain Monte Carlo (MCMC) sampling.", "findings": "The model successfully synthesised sparse data, revealing a pooled mean failure rate of 0.12 failures per operational year (95% credible interval: 0.09, 0.16). Crucially, the hierarchical structure showed that site-specific operational environments contributed to 35% of the variance in observed reliability, a key factor masked by non-hierarchical analyses.", "conclusion": "The Bayesian hierarchical model provides a statistically robust framework for reliability assessment under data-scarce conditions, offering a significant improvement over deterministic or non-hierarchical probabilistic methods. It effectively quantifies both central tendencies and contextual variability in system performance.", "recommendations": "Adoption of this modelling approach is recommended for asset management planning within the region. Future work should integrate covariate data on environmental stressors and maintenance practices to further refine the model's predictive capability.", "key words": "Bayesian statistics, hierarchical modelling, reliability engineering, process control, predictive maintenance, industrial systems", "contribution statement