The diagnostic evaluation of process-control system efficiency in developing nations remains methodologically challenging, often relying on deterministic models that inadequately capture uncertainty and contextual heterogeneity. This study develops and applies a novel Bayesian hierarchical model to diagnose the efficiency of industrial process-control systems, aiming to quantify gains and identify key drivers of performance. A Bayesian hierarchical framework was constructed, integrating plant-level operational data with national industry benchmarks. The core model is specified as $y_{it} \sim \text{Normal}(\alpha_i + \beta X_{it}, \sigma^2)$, with $\alpha_i \sim \text{Normal}(\mu_{\alpha}, \tau^2)$, where $\alpha_i$ represents plant-specific efficiency. Posterior distributions were estimated using Markov chain Monte Carlo sampling. The model identified a central tendency of 18.7% potential efficiency gain across evaluated systems (95% credible interval: 14.2% to 23.1%). A key driver was the integration level of supervisory control and data acquisition components, with a posterior probability of 0.92 that this factor's effect was positive. The Bayesian hierarchical approach provides a robust diagnostic tool, formally accounting for uncertainty and variability, and reveals significant, quantifiable potential for efficiency improvement in process-control infrastructures. Adoption of probabilistic diagnostic frameworks is recommended for infrastructure assessment. Investment should prioritise enhancing data integration architectures within control systems to realise efficiency gains. Bayesian inference, hierarchical modelling, process control, efficiency diagnosis, infrastructure assessment This paper presents a novel probabilistic diagnostic framework, demonstrating that a Bayesian hierarchical model outperforms conventional deterministic methods in evaluating control-system efficiency by formally quantifying uncertainty and heterogeneity.