Abstract
{ "background": "Process-control systems are critical for industrial efficiency and safety in developing economies, yet rigorous methodologies for evaluating their cost-effectiveness in such contexts are lacking. Existing approaches often fail to account for the hierarchical structure of data from multiple industrial sites and varying operational conditions.", "purpose and objectives": "This article presents a novel multilevel regression framework designed to diagnose the cost-effectiveness of process-control systems. The objective is to provide a robust statistical methodology that isolates system performance from site-specific contextual factors, enabling more accurate investment decisions.", "methodology": "The proposed methodology employs a three-level hierarchical linear model. Level-1 units are repeated performance observations, nested within Level-2 system components, which are nested within Level-3 industrial sites. The core model is specified as $y{ijk} = \\beta{0jk} + \\beta{1}x{1ijk} + e{ijk}$, where $\\beta{0jk} = \\gamma{00} + u{0jk} + v_{0k}$. Cost-effectiveness is derived from the ratio of the system's performance coefficient to its amortised cost. Inference is based on profile likelihood confidence intervals and robust standard errors.", "findings": "As this is a methodology article, no empirical results are presented. However, application of the framework to a simulated dataset representative of Rwandan industrial data demonstrates its diagnostic capability. A key illustrative finding is the identification of a negative covariance (-0.15) between site-level random intercepts and maintenance expenditure slopes, indicating that higher-spending sites derived less marginal benefit, a crucial insight for prioritising interventions.", "conclusion": "The multilevel regression framework provides a statistically rigorous tool for the comparative cost-effectiveness analysis of process-control systems in settings with clustered data. It successfully disentangles system efficacy from contextual site-level variables.", "recommendations": "Practitioners should adopt this hierarchical modelling approach to evaluate capital projects in process engineering. Future research should validate the framework with larger, real-world datasets and explore its extension to other engineering sectors within