Abstract
{ "background": "Process-control systems in the manufacturing sector are critical for operational efficiency and product yield. In the Nigerian context, evaluating the effectiveness of such systems is often hampered by data scarcity, process variability, and the need to integrate information from multiple, heterogeneous production lines.", "purpose and objectives": "This case study presents and methodologically evaluates a Bayesian hierarchical model designed to quantify yield improvement attributable to enhanced process-control systems. The objective is to provide a robust analytical framework suitable for environments with limited but structured data.", "methodology": "A case study approach was adopted, applying the model to anonymised production data from three Nigerian manufacturing plants. The core model is a Bayesian hierarchical linear regression: $y{ij} \\sim \\text{Normal}(\\alphaj + \\betaj x{ij}, \\sigma^2)$, with $\\alphaj \\sim \\text{Normal}(\\mu\\alpha, \\tau\\alpha^2)$ and $\\betaj \\sim \\text{Normal}(\\mu\\beta, \\tau\\beta^2)$, where $i$ indexes batches and $j$ indexes plants. Posterior distributions were estimated using Markov chain Monte Carlo sampling.", "findings": "The model successfully integrated data across plants, providing stable estimates despite sparse individual plant data. A key finding was a central estimate of the mean yield improvement coefficient ($\\mu\\beta$) of 0.18, with a 90% credible interval of [0.11, 0.25], indicating a statistically meaningful positive effect. The hierarchical structure showed substantial variation in plant-level intercepts ($\\alphaj$), highlighting differing baseline efficiencies.", "conclusion": "The Bayesian hierarchical model offers a methodologically sound approach for assessing process-control interventions in settings with constrained data. It formally accounts for both shared effects and inherent heterogeneity across production units.", "recommendations": "Practitioners should adopt hierarchical modelling to pool information for more reliable inference. Future research should apply the framework to a broader set of industries