Efficient Hierarchical Latent Gaussian Models for Heterogeneous and Skewed IoT Reliability Data

The reliability of Internet of Things systems is critical for industrial applications; however, operational reliability data are often heterogeneous and strongly right-skewed, exhibiting non-Gaussian behaviour, overdispersion, and production-level variability that challenge classical predictive maintenance models. Existing approaches frequently rely on pooled assumptions or simplified error structures, limiting their ability to identify latent batch-level degradation and to jointly interpret discrete failure events and continuous lifetime information. To address these limitations, this study proposes a hierarchical Bayesian framework based on Integrated Nested Laplace Approximation (INLA) to jointly model discrete reset counts and continuous failure times. Three Latent Gaussian Models are evaluated—ranging from pooled baseline specifications to a fully joint model with shared latent batch effects—using a synthetic dataset designed to mimic realistic industrial fault patterns. The analysis demonstrates that standard pooled models fail to capture the degradation dynamics of defective device batches. In contrast, the hierarchical joint model successfully recovers latent quality variations, accurately links high reset intensity with shortened lifetimes, and substantially improves model fit, achieving a DIC reduction of over 67% compared to baseline approaches. INLA provides a computationally efficient and rigorously calibrated alternative to MCMC-based methods for modelling skewed and heterogeneous reliability data. The proposed framework enables reliable identification of defective production batches and robust uncertainty quantification, offering a practical tool for data-driven predictive maintenance in Industry 4.0. Future work will focus on validating the proposed framework using real industrial IoT datasets.