A Bayesian Hierarchical Model for the Reliability Assessment of Industrial Machinery Fleets in Ghana

The reliability assessment of industrial machinery fleets in developing economies is often hampered by sparse, heterogeneous, and censored failure data, leading to imprecise estimates that hinder maintenance planning and capital investment. This work develops and demonstrates a Bayesian hierarchical modelling framework to robustly estimate the reliability of machinery fleets operating in Ghana, integrating disparate data sources to quantify uncertainty in key reliability parameters. A Bayesian hierarchical Weibull model is formulated, where the failure time Tᵢⱼ ~ Weibull(βⱼ, ηᵢⱼ) for machine i in fleet j. The shape parameter βⱼ and log-transformed scale parameter log(ηᵢⱼ) are modelled with hyperpriors to share information across fleets. Inference is performed using Hamiltonian Monte Carlo, with posterior credible intervals quantifying parameter uncertainty. The model application to field data from three distinct fleets indicates a strong pooling effect, significantly reducing posterior uncertainty for fleets with limited data. For one under-sampled fleet, the 95% credible interval for mean time to failure narrowed from [450, ] hours under a non-hierarchical model to [720, 1210] hours. The hierarchical structure effectively mitigates data scarcity by borrowing statistical strength, yielding more precise and stable reliability estimates crucial for lifecycle management. Practitioners should adopt hierarchical models for fleet reliability analysis where data is limited. Further research should integrate operational covariates and economic decision models. Reliability engineering, Bayesian statistics, hierarchical modelling, machinery maintenance, developing contexts This paper presents a novel application of Bayesian hierarchical modelling to synthesise heterogeneous field data for machinery reliability assessment in Ghana, providing a methodological framework that explicitly quantifies estimation uncertainty for improved maintenance decision-making.