Nigeria's district hospitals play a crucial role in healthcare delivery but face significant challenges in maintaining system reliability. A comprehensive meta-analysis approach was employed to evaluate the performance of district hospitals across different regions. The study utilised panel-data estimation techniques, including fixed effects models to account for individual hospital characteristics and time-invariant confounders. Panel-data estimates revealed a significant variation in system reliability among districts (p < 0.05), with some areas showing an improvement trend over the past five years. This study highlights the need for targeted interventions to enhance the reliability of district hospitals, particularly in regions where there is evidence of positive change. Policy-makers should prioritise funding and training programmes aimed at improving infrastructure and staff competence in selected districts identified as showing improvement trends. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.