Abstract
{ "background": "The industrial sector in Ethiopia has undergone significant expansion, yet systematic, data-driven diagnostics of manufacturing systems efficiency remain underdeveloped. Existing methods often fail to account for plant-level heterogeneity and the hierarchical structure of industrial data, limiting actionable insights for engineering management.", "purpose and objectives": "This study aims to develop and validate a novel Bayesian hierarchical model to diagnose efficiency in manufacturing systems, quantifying gains and identifying key drivers of performance variation across plants and subsectors.", "methodology": "We formulate a Bayesian hierarchical model where the efficiency $\eta{ij} = \\exp(-u{ij})$ for plant $i$ in group $j$ is modelled with $u{ij} \\sim \\text{Half-Normal}^{+}(\\sigmaj)$, and group-level parameters $\\sigmaj$ follow a hyperprior $\\sigmaj \\sim \\text{Inverse-Gamma}(\\alpha, \\beta)$. Inference uses Hamiltonian Monte Carlo, with model fit assessed via posterior predictive checks and Watanabe-Akaike information criterion.", "findings": "The model identified substantial inter-plant efficiency variation, with a posterior probability of 0.92 that the textile subsector's efficiency dispersion parameter exceeded that of agro-processing. Estimated median efficiency gains from targeting the worst-performing decile of plants exceeded 15 percentage points.", "conclusion": "The proposed model provides a robust diagnostic framework, successfully capturing multi-level efficiency dynamics within the manufacturing sector and offering a superior fit compared to conventional, non-hierarchical approaches.", "recommendations": "Industrial policy and plant management should adopt hierarchical diagnostic tools to prioritise interventions. Future research should integrate real-time operational data into the modelling framework for dynamic efficiency monitoring.", "key words": "Bayesian inference, efficiency diagnostics, hierarchical modelling, industrial engineering, manufacturing systems, stochastic frontiers", "contribution statement": "This paper introduces a novel Bayesian hierarchical stochastic frontier model, specifically tailored for the diagnostic analysis of manufacturing systems, and provides the first application yielding plant- and subsector-level efficiency estimates