Abstract
{ "background": "The reliability assessment of process-control systems in industrial settings is critical for operational safety and efficiency. In many developing nations, such assessments are hindered by sparse, heterogeneous data and a lack of methodologies that formally account for operational uncertainty and variability across different sites.", "purpose and objectives": "This study presents and evaluates a novel Bayesian hierarchical modelling framework designed to quantify the reliability of such systems within a data-scarce context. The primary objective is to provide a robust methodological tool that integrates multi-source operational data to produce more accurate and interpretable reliability estimates.", "methodology": "A Bayesian hierarchical model was developed, formalised as $\\lambda{ij} \\sim \\text{Gamma}(\\alphai, \\betai)$, $\\alphai, \\betai \\sim \\text{LogNormal}(\\mu{\\alpha,\\beta}, \\sigma^2{\\alpha,\\beta})$, where $\\lambda{ij}$ is the failure rate for system $j$ in plant $i$. The model parameters were estimated using Markov Chain Monte Carlo simulation, with data aggregated from maintenance logs and performance tests across multiple industrial facilities.", "findings": "The model successfully synthesised disparate data sources, yielding plant-specific reliability estimates with quantified uncertainty. A key finding was that the posterior distribution for the mean time between failures (MTBF) across all sites had a 95% credible interval of 450 to 520 hours, which was 15-20% wider than estimates from traditional pooled analysis, highlighting greater underlying variability. The hierarchical structure revealed significant inter-plant heterogeneity in failure rates.", "conclusion": "The proposed Bayesian hierarchical model offers a statistically rigorous framework for reliability assessment under data constraints, effectively capturing and distinguishing between common population trends and site-specific variations. It represents a substantial methodological advance over conventional, non-hierarchical approaches in this context.", "recommendations": "Adoption of this modelling framework is recommended for asset management and regulatory review processes where data are limited and heterogeneous. Future work should focus