Abstract
{ "background": "The reliability of electrical infrastructure is critical for economic development. In South Africa, ageing power-distribution equipment and inconsistent adoption of modern systems pose significant challenges to grid stability and expansion. Existing evaluation methods often lack the capacity to integrate sparse, heterogeneous data and quantify uncertainty in adoption forecasts.", "purpose and objectives": "This study aimed to develop and apply a novel Bayesian hierarchical model to evaluate the adoption rates of key power-distribution equipment, specifically transformers and ring main units, across the national network. The objective was to provide probabilistic forecasts of adoption to inform infrastructure investment and policy.", "methodology": "A Bayesian hierarchical model was constructed to analyse adoption data across multiple provinces and municipalities. The core model structure is $y{it} \\sim \\text{Binomial}(n{it}, \\theta{it})$, $\\text{logit}(\\theta{it}) = \\alphai + \\beta X{it} + \\epsilont$, with $\\alphai \\sim \\text{Normal}(\\mu{\\alpha}, \\sigma{\\alpha})$, where $y_{it}$ represents adopted units in area $i$ at time $t$. Weakly informative priors were used, and posterior distributions were estimated using Markov chain Monte Carlo sampling.", "findings": "The model estimates revealed substantial regional heterogeneity, with posterior credible intervals for provincial-level adoption rates remaining wide, indicating high uncertainty. A key concrete finding is that the adoption rate for modern vacuum-interruption ring main units is projected to reach only 34% (95% Credible Interval: 28–41%) by the end of the forecast period, underscoring a slow transition from older technologies.", "conclusion": "The Bayesian hierarchical framework successfully quantified the uncertainty in equipment adoption, revealing that current adoption trajectories are insufficient for rapid national infrastructure modernisation. The slow pace threatens long-term grid reliability and capacity.", "recommendations": "Infrastructure planning must account for pronounced regional disparities. Policy should target incentives in lagging regions and prioritise