A Bayesian Hierarchical Model for the Cost-Effectiveness Evaluation of Power-Distribution Equipment in Ghana

{ "background": "Evaluating the cost-effectiveness of power-distribution equipment in developing grids is complex, requiring the integration of sparse, heterogeneous data on costs, failure rates, and local operational conditions. Traditional deterministic models often fail to adequately quantify uncertainty, which is critical for robust infrastructure investment planning.", "purpose and objectives": "This article presents a novel Bayesian hierarchical modelling framework designed to quantify the cost-effectiveness of distribution equipment, such as transformers and switchgear, while formally incorporating parameter uncertainty and variability across different operational districts.", "methodology": "The methodology integrates life-cycle cost data and reliability metrics within a hierarchical structure. The core model is specified as $y{ij} \\sim \\text{Gamma}(\\alpha{j}, \\beta{j})$, where $\\alpha{j}, \\beta{j} \\sim \\text{Normal}(\\mu{\\alpha,\\beta}, \\sigma^{2}{\\alpha,\\beta})$, with $y{ij}$ representing the cost-effectiveness ratio for asset $i$ in region $j$. Parameters are estimated using Hamiltonian Monte Carlo sampling, providing full posterior distributions for inference.", "findings": "The application to a Ghanaian case study demonstrates the model's utility, revealing that posterior distributions for the cost-effectiveness of pole-mounted transformers showed considerable variance, with the 95% credible interval for the mean ratio spanning from 0.85 to 1.42. This indicates a significant probability that certain equipment types are not cost-optimal under current conditions.", "conclusion": "The Bayesian hierarchical model provides a statistically rigorous framework for cost-effectiveness analysis, offering a substantial improvement over point-estimate approaches by fully characterising uncertainty. It is particularly suited to data-scarce environments common in infrastructure planning.", "recommendations": "Utility planners should adopt probabilistic frameworks that explicitly model uncertainty. Future research should integrate predictive maintenance data and climate resilience factors into the hierarchical model structure to enhance its decision-support capability.", "key words": "Bayesian inference, hierarchical modelling, cost-benefit