This case study evaluates the operational efficiency of district hospitals in Kenya by applying time-series forecasting models to measure yield improvement. Time-series forecasting models were employed to analyse hospital data over a five-year period. The Box-Jenkins methodology was used, where the ARIMA model was specified as $ARIMA(p,d,q)$, and uncertainty in predictions is quantified using robust standard errors. The analysis revealed an average annual yield improvement of 7% across all districts, with significant variability by region, indicating a need for targeted interventions to optimise resource utilization. Time-series forecasting models effectively identified trends and predicted future performance in district hospitals, highlighting the importance of regional-specific strategies for improvement. District health authorities are recommended to implement evidence-based management practices guided by predictive models, focusing on regions with lower yield improvements to maximise overall system efficiency.