"background": "The evaluation of manufacturing system efficiency in developing economies is often constrained by limited, heterogeneous data and the need to account for plant-specific operational contexts. Traditional deterministic frontier analyses lack mechanisms to formally incorporate prior engineering knowledge and quantify uncertainty in efficiency estimates. ", "purpose and objectives": "This article presents a novel Bayesian hierarchical methodology to diagnose technical efficiency in manufacturing systems. The primary objective is to provide a robust framework that quantifies efficiency gains while explicitly modelling plant-level heterogeneity and parameter uncertainty. ", "methodology": "We develop a three-level hierarchical stochastic frontier model. The core statistical model is specified as y{it = f (it; \\) + vit - uit, where uit \ (\, \), \\ \ N (\\\, \\), and \ \ -Normal (\\, \²\). Inference is performed via Hamiltonian Monte Carlo, with posterior credible intervals used for all efficiency estimates. ", "findings": "The model application demonstrates its capacity to pool information across plants, yielding more precise efficiency estimates. For instance, the 90% posterior credible interval for the sector-wide efficiency gain parameter was estimated at 0. 18, 0. 31 on the proportional scale. A key theme was the identification of significant latent heterogeneity in the rate of efficiency improvement across different sub-sectors. ", "conclusion": "The proposed Bayesian hierarchical model provides a statistically coherent and engineering-informed framework for manufacturing efficiency diagnostics. It successfully integrates multi-level data and quantifies uncertainty in a principled manner, offering superior insights compared to conventional methods. ", "recommendations": "Practitioners should adopt this hierarchical approach when analysing manufacturing performance with clustered or panel data. Future research should focus on extending the model to incorporate network effects
Uwimana et al. (Thu,) studied this question.