This study addresses a current research gap in Engineering concerning Biomedical Engineering Innovations for Diagnostic Devices in Resource-Limited Settings in Tanzania. The objective is to formulate a rigorous model, state verifiable assumptions, and derive results with direct analytical or practical implications. A structured analytical approach was used, integrating formal modelling with domain evidence. The results establish bounded error under perturbation, a convergent estimation process under stated assumptions, and a stable link between the proposed metric and observed outcomes. The findings provide a reproducible analytical basis for subsequent theoretical and applied extensions. Stakeholders should prioritise inclusive, locally grounded strategies and improve data transparency. Biomedical Engineering Innovations for Diagnostic Devices in Resource-Limited Settings, Tanzania, Africa, Engineering, case study This work contributes a formal specification, transparent assumptions, and mathematically interpretable claims. The maintenance outcome was modelled as $Y_{it}=\beta_0+\beta_1X_{it}+u_i+\varepsilon_{it}$, with robustness checked using heteroskedasticity-consistent errors.