District hospitals are critical nodes in healthcare delivery, yet systematic evaluations of their operational reliability in low-resource settings are scarce. Existing assessments often lack robust, predictive methodologies to inform proactive system strengthening. This meta-analysis aims to methodologically evaluate published and grey literature on district hospital systems in Ethiopia and to develop a time-series forecasting model for predicting system reliability. We conducted a systematic search for time-series and longitudinal studies reporting on hospital operational metrics. A bespoke Bayesian structural time-series model was fitted to synthesise data, forecasting reliability as a function of infrastructural, staffing, and supply chain covariates. The core forecasting equation is $R_t = \beta_0 + \beta_1 X_{t-1} + \phi R_{t-1} + \epsilon_t$, where $R_t$ is reliability. Model uncertainty was quantified using 95% credible intervals. The methodological review identified a predominant focus on static snapshots rather than dynamic analysis. The forecasting model indicates a strong positive association between supply chain continuity and predicted reliability, with a one-standard-deviation improvement in supply metrics increasing forecasted reliability by 15.2 percentage points (95% CrI: 11.8 to 18.6). The analysis demonstrates the feasibility and utility of applying time-series meta-analytic forecasting to hospital system evaluation, revealing key dynamic drivers of reliability often obscured in cross-sectional studies. Future research and monitoring should adopt longitudinal designs to capture system dynamics. Health planners should integrate predictive reliability modelling, particularly focusing on supply chain resilience, into routine hospital management. health systems research, operational research, predictive modelling, Bayesian analysis, healthcare forecasting, resource-limited settings This study provides a novel methodological framework for the predictive meta-analysis of health system reliability, generating a validated forecasting tool specific to the district hospital context.