A Bayesian Hierarchical Model for Yield Improvement Diagnostics in Ghanaian Manufacturing Systems

{ "background": "Persistent yield inefficiencies in manufacturing systems represent a critical barrier to industrial productivity and economic development. Current diagnostic methods often lack the statistical rigour to disentangle plant-level effects from systemic process variations, particularly in contexts with heterogeneous operational data.", "purpose and objectives": "This working paper develops and evaluates a novel Bayesian hierarchical model specifically designed for yield improvement diagnostics. The objective is to provide a robust methodological framework for quantifying and attributing yield gains within complex, multi-plant manufacturing environments.", "methodology": "We propose a Bayesian hierarchical model where yield $Y{ij} \\sim \\text{Beta}(\\mu{ij}\\phi, (1-\\mu{ij})\\phi)$, with $\\text{logit}(\\mu{ij}) = \\alpha + \\beta X{ij} + ui$, and $ui \\sim N(0, \\sigma^2u)$. Here, $u_i$ represents the random effect for plant $i$. Inference is performed via Hamiltonian Monte Carlo, with posterior credible intervals used for uncertainty quantification.", "findings": "The model application to a case study demonstrates its diagnostic capability, isolating a dominant systemic factor accounting for approximately 60% of the explainable yield variance. Posterior distributions indicate a 95% credible interval of [0.12, 0.19] for the key process parameter $\\beta$, confirming a positive but uncertain effect.", "conclusion": "The Bayesian hierarchical framework offers a statistically principled approach for yield diagnostics, effectively partitioning variation and quantifying uncertainty in performance attribution.", "recommendations": "Manufacturing engineers and plant managers should adopt hierarchical modelling for systematic yield analysis. Further research should integrate real-time data streams to transition from diagnostic to predictive yield management.", "key words": "Bayesian inference, hierarchical modelling, manufacturing yield, process diagnostics, industrial engineering, probabilistic modelling", "contribution statement": "This paper introduces a novel application of Bayesian hierarchical modelling for manufacturing yield diagnostics, providing a new method to attribute