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

"background": "Persistent yield inefficiencies in manufacturing systems represent a critical barrier to industrial development. Current diagnostic methods often rely on aggregated data, failing to account for plant-specific variability and the hierarchical nature of production processes, which limits actionable insights for improvement. ", "purpose and objectives": "This study develops and validates a novel Bayesian hierarchical model to diagnose the sources of yield variation and quantify improvement potential within complex, multi-plant manufacturing environments. The objective is to provide a robust, probabilistic framework for identifying systemic versus localised inefficiencies. ", "methodology": "The proposed model structures yield Y{ij for batch j in plant i as Yij \ (\, \²), with plant-level means \ \ (\, \²). This explicitly separates within-plant and plant variance components. Inference was performed using Hamiltonian Monte Carlo, applied to operational data from multiple plants. ", "findings": "The model identified substantial plant heterogeneity, with the estimated global mean yield \ at 0. 72 (95% credible interval: 0. 68 to 0. 76). Crucially, the posterior distribution for \² indicated that approximately 40% of the total yield variation was attributable to systemic differences between plants, rather than within-plant operational noise. ", "conclusion": "The Bayesian hierarchical model successfully disentangles sources of yield loss, demonstrating that a significant portion of inefficiency is rooted in systemic, plant-level factors. This moves diagnosis beyond simple averages to a probabilistic assessment of improvement levers. ", "recommendations": "Manufacturing managers should adopt hierarchical diagnostic frameworks to prioritise interventions. Resource allocation should target underperforming plants identified by the model's posterior estimates, focusing on standardising superior practices across sites. ", "key words": "Bayesian inference, hierarchical modelling, manufacturing yield,