{ "background": "District hospital systems in Tanzania face persistent challenges in resource allocation and service delivery due to unpredictable demand and systemic constraints. System reliability, defined as the consistent provision of intended healthcare services, is critical for public health outcomes but remains difficult to quantify and forecast effectively.", "purpose and objectives": "This systematic review evaluates methodological approaches used to assess district hospital system reliability in Tanzania, with a specific objective to synthesise and critique time-series forecasting models applied in this context. It aims to identify robust methodological frameworks and gaps in current predictive analytics.", "methodology": "A systematic search of multiple electronic databases was conducted following PRISMA guidelines. Studies were screened against pre-defined inclusion criteria focusing on methodological designs and quantitative models for forecasting healthcare system performance metrics. Quality assessment was performed using a modified Cochrane risk-of-bias tool for methodological evaluations.", "findings": "The review identified a predominant reliance on autoregressive integrated moving average (ARIMA) models, represented generally as $Xt = c + \\sum{i=1}^{p}\\phii X{t-i} + \\epsilont + \\sum{i=1}^{q}\\thetai \\epsilon{t-i}$, for forecasting bed occupancy and drug stock-outs. However, a significant methodological gap was the frequent omission of uncertainty quantification; fewer than 30% of studies employing these models reported prediction intervals or conducted robustness checks on their forecasts.", "conclusion": "Existing methodological applications for forecasting hospital system reliability are narrowly focused on a limited set of statistical techniques and often lack rigorous validation and uncertainty analysis, limiting their utility for strategic planning.", "recommendations": "Future research should integrate exogenous variables (e.g., climatic, demographic) into hybrid forecasting models and mandate the reporting of prediction intervals. Capacity building in advanced statistical modelling for health system researchers is urgently needed.", "key words": "health systems research, predictive modelling, ARIMA, resource planning, healthcare operations, uncertainty quantification", "contribution statement": "This review provides the first dedicated methodological synthesis of time-series