{ "background": "Water treatment systems in South Africa face persistent challenges in operational efficiency and resource optimisation. Current diagnostic methods for yield improvement often lack a formal framework for integrating multi-facility data and quantifying uncertainty, hindering targeted interventions.", "purpose and objectives": "This study aimed to develop and validate a novel Bayesian hierarchical model to diagnose and quantify the drivers of yield improvement across multiple water treatment facilities, providing a robust tool for performance evaluation.", "methodology": "A Bayesian hierarchical model was constructed, formalised as $y{ij} \\sim \\text{Normal}(\\alphaj + \\beta X{ij}, \\sigma^2)$, with $\\alphaj \\sim \\text{Normal}(\\mu{\\alpha}, \\tau^2)$, where $y{ij}$ is the yield measurement for facility $j$, $X{ij}$ are covariates, and $\\alphaj$ represents the facility-specific intercept. The model was applied to operational data from a network of treatment plants, using Markov chain Monte Carlo methods for inference.", "findings": "The model identified chemical dosing optimisation as the most significant driver of yield improvement, with a posterior probability exceeding 0.95. Facility-specific random effects revealed a pronounced performance gap, where the highest-performing quartile of facilities achieved yields approximately 18% greater than the lowest quartile, after accounting for covariates.", "conclusion": "The proposed model provides a statistically rigorous diagnostic framework that successfully disentangles common from facility-specific factors affecting yield, offering a superior alternative to aggregated analyses.", "recommendations": "Adoption of this modelling approach is recommended for systemic performance benchmarking. Utilities should prioritise interventions targeting chemical process control, informed by the facility-level posterior estimates generated by the model.", "key words": "Bayesian inference, hierarchical modelling, water treatment efficiency, performance diagnostics, operational yield", "contribution statement": "This paper presents a novel application of Bayesian hierarchical modelling for facility-level performance diagnostics in water treatment, delivering a new tool that quantifies uncertainty