A Bayesian Hierarchical Model for the Cost-Effectiveness of Process-Control Systems in South Africa: A Methodological Evaluation, 2000–2026

{ "background": "The evaluation of process-control systems in structural engineering projects often relies on deterministic cost-benefit analyses, which fail to adequately account for variability in project parameters and inherent uncertainties in long-term performance data.", "purpose and objectives": "This study presents a novel Bayesian hierarchical modelling framework to assess the cost-effectiveness of these systems. The primary objective is to provide a robust methodological evaluation that quantifies uncertainty and integrates heterogeneous data sources.", "methodology": "A Bayesian hierarchical model was developed, formalised as $y{ij} \\sim \\text{Normal}(\\alphaj + \\beta X{ij}, \\sigma^2)$, $\\alphaj \\sim \\text{Normal}(\\mu{\\alpha}, \\tau^2)$, where $y{ij}$ is the cost-effectiveness ratio for project $i$ in region $j$. The model incorporates prior distributions from expert elicitation and historical project data. Posterior distributions were estimated using Markov chain Monte Carlo simulation.", "findings": "The model indicates a high probability (posterior probability > 0.85) that centralised, automated systems yield superior long-term cost-effectiveness compared to decentralised analogues. A key finding is that for every 10% increase in system integration complexity, the median cost-effectiveness ratio improves by approximately 15%, with a 95% credible interval of [11%, 19%].", "conclusion": "The Bayesian hierarchical framework offers a statistically rigorous method for cost-effectiveness analysis, explicitly characterising uncertainty and enabling probabilistic decision-making for engineering project investment.", "recommendations": "Adoption of this modelling approach is recommended for future infrastructure project appraisals. Further research should focus on expanding the prior data set to include a wider range of structural system types.", "key words": "Bayesian inference, cost-benefit analysis, structural systems, probabilistic modelling, decision support", "contribution statement": "This paper provides a novel methodological framework that integrates multi-level project data within a probabilistic model, offering a significant advance over traditional deterministic