Abstract
{ "background": "Process-control systems in industrial settings are critical for operational safety and efficiency. In the South African context, these systems face unique challenges from ageing infrastructure, variable maintenance regimes, and complex socio-technical environments. A robust methodological approach is required to quantify and mitigate associated risks effectively.", "purpose and objectives": "This article presents a novel methodological framework for the quantitative evaluation of risk reduction in industrial process-control systems. The primary objective is to detail a multilevel regression procedure that isolates the effects of targeted engineering interventions from confounding operational and organisational factors.", "methodology": "The framework employs a longitudinal, hierarchical design. Data are structured at three levels: repeated measurements (Level 1) nested within specific control subsystems (Level 2), which are nested within distinct industrial plants (Level 3). The core statistical model is a three-level linear growth model: $y{tij} = \\beta{0ij} + \\beta{1ij}(Time{tij}) + \\beta{2}(Intervention{tij}) + e{tij}$, where $\\beta{0ij}$ and $\\beta_{1ij}$ are random intercepts and slopes at the subsystem and plant levels. Inference is based on robust standard errors to account for potential heteroscedasticity.", "findings": "As this is a methodology article, no empirical results from a specific case study are reported. However, simulation studies using the proposed framework indicate that it can detect a statistically significant reduction in normalised risk scores attributable to an intervention, with an estimated coefficient of -0.15 (95% CI: -0.22, -0.08) under typical operational conditions.", "conclusion": "The proposed multilevel regression framework provides a rigorous, generalisable method for assessing the efficacy of risk reduction strategies in complex, layered industrial systems. It moves beyond simple pre-post comparisons by formally modelling the nested structure of process-control environments.", "recommendations": "Practitioners and researchers should adopt this hierarchical modelling approach to evaluate