A Comparative Bayesian Hierarchical Modelling Approach to Industrial Machinery Fleet Reliability in Kenya, 2000–2024

{ "background": "Industrial machinery fleet reliability is a critical determinant of productivity and economic growth in developing economies. Traditional reliability models often fail to account for the heterogeneity and sparse failure data characteristic of such fleets, leading to inaccurate maintenance forecasts and resource allocation.", "purpose and objectives": "This study aims to develop and validate a novel Bayesian hierarchical modelling framework for comparative reliability analysis of heterogeneous industrial machinery fleets. The objective is to provide a robust, data-adaptive method for quantifying system reliability and its associated uncertainties.", "methodology": "A comparative study was conducted using maintenance and failure data from multiple industrial sectors. The core methodological innovation is a Bayesian hierarchical model specified as $\\lambda{ij} \\sim \\text{Gamma}(\\alphaj, \\betaj)$, where $\\lambda{ij}$ is the failure rate for machine $i$ in fleet $j$, with fleet-level parameters $\\alphaj, \\betaj$ drawn from a common hyperprior distribution. Model inference was performed using Markov Chain Monte Carlo (MCMC) sampling.", "findings": "The Bayesian hierarchical model demonstrated superior predictive performance compared to fleet-agnostic models, with a 95% credible interval for the pooled failure rate across all fleets estimated at [0.021, 0.034] failures per operational hour. A key finding was the identification of a distinct reliability cluster within the agricultural machinery fleet, showing a 40% higher mean time between failures than the manufacturing sector cluster.", "conclusion": "The proposed Bayesian hierarchical framework provides a statistically rigorous and practically useful tool for fleet reliability assessment, effectively handling data sparsity and heterogeneity. It offers a paradigm shift from deterministic or pooled estimates to probabilistic, fleet-stratified reliability forecasting.", "recommendations": "Adoption of this modelling approach is recommended for asset managers and policymakers to inform targeted maintenance strategies and capital investment planning. Future work should integrate operational context variables, such as environmental conditions and operator skill levels, into the hierarchical structure.", "key words": "Bayesian hierarchical model