The healthcare landscape in Ethiopia presents significant challenges, particularly in rural and underserved districts where infrastructure is often limited. Time-series analysis was employed using ARIMA (AutoRegressive Integrated Moving Average) model for predicting hospital system performance across Ethiopian districts. A prediction error rate of ±10% in the ARIMA model indicated a reliable forecast, with some hospitals showing improvement trends over two years. The ARIMA models successfully forecasted system reliability, offering insights into potential areas for intervention and resource distribution among district hospitals. District health authorities should prioritise investment in these systems based on the reliability forecasts to ensure equitable healthcare access. Time-series forecasting, ARIMA model, System Reliability, Ethiopian District Hospitals Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.