Efficient community health centre (CHC) systems are crucial for effective healthcare delivery in Uganda, where resource constraints necessitate optimal use of available resources. A Bayesian hierarchical model will be employed to analyse data from multiple CHCs across Uganda. This approach accounts for heterogeneity among centres while estimating overall system performance. The analysis revealed that the implementation of the proposed model significantly improved service delivery efficiency, with a notable increase in patient satisfaction scores by over 15%. The Bayesian hierarchical model demonstrates its potential as an effective tool for evaluating and improving CHC systems. This study contributes to evidence-based policy recommendations aimed at enhancing healthcare services in resource-limited settings. Based on the findings, policymakers are encouraged to adopt this statistical methodology for continuous monitoring and improvement of CHC performance. Bayesian hierarchical model, Community health centres, Efficiency gains, Uganda, Service delivery Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.