District hospitals in Tanzania play a crucial role in healthcare delivery but face challenges in resource allocation and service quality. The study employed systematic search strategies across databases including PubMed and Web of Science. Data were analysed using Bayesian hierarchical models with uncertainty quantification through credible intervals. A significant proportion (45%) of district hospitals showed positive yield improvements, indicating potential for methodological enhancements. Bayesian hierarchical models provide a robust framework for evaluating district hospital systems in Tanzania, highlighting the importance of data-driven decision-making. District health authorities should consider adopting these models to improve service delivery and resource management. Tanzania, District Hospitals, Bayesian Hierarchical Models, Yield Improvement, Resource Allocation Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.