{ "background": "Manufacturing systems in Uganda face persistent challenges in achieving consistent product yield, with diagnostic efforts often hampered by fragmented data and complex, multi-level process interactions. Existing analytical methods frequently lack the flexibility to model plant-specific variability while enabling inference across a sector.", "purpose and objectives": "This article presents a novel Bayesian hierarchical modelling framework designed to diagnose and quantify the drivers of yield improvement in such contexts. Its objective is to provide a robust, unified methodology for separating systemic effects from plant-specific operational factors.", "methodology": "The proposed framework models yield $Y{ij}$ for batch $i$ in plant $j$ as $Y{ij} \\sim \\text{Normal}(\\muj, \\sigma^2)$, with plant-level means $\\muj \\sim \\text{Normal}(\\gamma0 + \\gamma1 Xj, \\tau^2)$. Here, $Xj$ represents plant-level covariates. Inference uses Hamiltonian Monte Carlo to estimate posterior distributions for all parameters, explicitly quantifying uncertainty in improvement estimates.", "findings": "Application to a multi-plant case study demonstrates the model's diagnostic capability, revealing that approximately 70% of the observed yield variation was attributable to differences in raw material quality protocols. Posterior probability intervals for key parameters were precisely estimated, indicating a high degree of confidence in the identified drivers.", "conclusion": "The framework provides a statistically rigorous and operationally actionable tool for yield diagnostics in complex manufacturing environments. It successfully integrates disparate data sources to isolate influential factors at appropriate hierarchical levels.", "recommendations": "Manufacturing engineers and plant managers should adopt hierarchical modelling approaches to move beyond aggregate yield metrics. Further research should integrate real-time sensor data into the model's structure for dynamic diagnostics.", "key words": "Bayesian inference, hierarchical model, manufacturing yield, process diagnostics, uncertainty quantification, industrial engineering", "contribution statement": "This paper introduces a novel, generalisable modelling framework that formally incorporates multi-level uncertainty for manufacturing diagnostics, a methodological advance