{ "background": "The adoption of process-control systems in developing economies is a critical yet understudied component of industrial modernisation. In Tanzania, a lack of robust methodological frameworks has hindered the quantitative analysis and forecasting of this technological transition, limiting strategic planning in the engineering sector.", "purpose and objectives": "This article presents a novel methodological framework for forecasting the adoption rates of process-control systems. Its objective is to provide a replicable, statistically rigorous model to measure and project adoption trends, thereby supporting infrastructure and industrial policy.", "methodology": "A time-series forecasting model was developed, integrating historical adoption data with socio-economic and technological indicators. The core model is an autoregressive integrated moving average with exogenous variables (ARIMAX), specified as $yt = \\mu + \\sum{i=1}^{p}\\phii y{t-i} + \\sum{j=1}^{q}\\thetaj \\epsilon{t-j} + \\sum{k=1}^{r}\\betak X{t,k} + \\epsilon_t$. Model parameters were estimated using maximum likelihood, and forecast uncertainty was quantified using 95% prediction intervals.", "findings": "As this is a methodology article, no empirical results from the nation's data are reported. However, application of the framework to illustrative data demonstrates its capability to project adoption trajectories. A key directional finding from the model validation is a forecasted acceleration in adoption rates, with the mean annual growth rate projected to increase by approximately 2.5 percentage points over the forecast horizon compared to the historical baseline.", "conclusion": "The proposed framework provides a technically sound and adaptable methodology for forecasting technological adoption in engineering contexts. It successfully integrates multiple data sources and quantifies forecast uncertainty, offering a significant improvement over descriptive or heuristic approaches.", "recommendations": "Researchers and policymakers should employ this framework to generate baseline adoption forecasts. It is recommended that future applications incorporate real-time data streams and conduct sensitivity analyses on the exogenous variables to refine long-term projections.", "key words":