Bayesian Hierarchical Modelling for Yield Improvement in Kenyan Manufacturing Systems: A Methodological Evaluation

{ "background": "Manufacturing systems in developing economies face persistent challenges in process yield, often due to heterogeneous plant-level conditions and data scarcity. Traditional quality control models frequently lack the flexibility to account for this operational variability, limiting their utility for targeted improvement.", "purpose and objectives": "This study presents a methodological evaluation of a Bayesian hierarchical model designed to measure and analyse yield improvement within a manufacturing context. The objective is to assess the model's capacity to provide robust, plant-specific inferences despite data limitations common in such settings.", "methodology": "A three-level hierarchical model was formulated, where yield $y{ij} \\sim \\text{Beta}(\\mu{ij}\\kappa, (1-\\mu{ij})\\kappa)$, with the logit of the mean $\\mu{ij}$ modelled as $\\text{logit}(\\mu{ij}) = \\alpha + \\betaj + \\gammai$. Here, $\\gammai$ represents machine-level random effects and $\\betaj$ plant-level effects. Inference was performed using Hamiltonian Monte Carlo, with posterior predictive checks used for model validation.", "findings": "The model successfully identified significant inter-plant variation, with the posterior distribution for the standard deviation of plant effects $\\betaj$ having a 95% credible interval of [0.42, 0.87] on the log-odds scale. A key theme was the model's ability to 'borrow strength' across the hierarchy, providing stable estimates for plants with sparse data, where a classical fixed-effects analysis failed to converge.", "conclusion": "The Bayesian hierarchical framework offers a statistically rigorous and operationally actionable methodology for yield analysis in environments with inherent heterogeneity and data constraints. It moves beyond aggregate assessment to facilitate plant-specific intervention strategies.", "recommendations": "Manufacturing engineers and quality managers should adopt hierarchical modelling approaches for plant performance benchmarking. Further research should integrate real-time sensor data into the model's observational layer to enhance predictive capability.", "key words": "Bay