Hierarchical Bayesian Intelligence Framework for Uncertainty Quantification and Reliability Assessment of Solid Oxide Fuel Cells

Solid oxide fuel cell (SOFC) stacks face reliability challenges because multiple degradation mechanisms interact with operational and environmental variability. We develop a hierarchical Bayesian framework that couples a monotone area-specific resistance (ASR) growth law with a Weibull time-to-failure model and employs a Student-t observation layer to down-weight outliers. Using multi-cell data, the approach narrows to 95% predictive-interval widths for ASR and lifetime by up to 33 % relative to a non-hierarchical baseline, and global sensitivity analysis identifies the ASR growth rate as the dominant driver (S<inline-formula> <tex-math notation="LaTeX">$1~\approx ~0.84$ </tex-math></inline-formula>). Scenario projections quantify operational effects: hot&#x2013;humid climates raise failure probability to <inline-formula> <tex-math notation="LaTeX">$\approx 56$ </tex-math></inline-formula> % versus <inline-formula> <tex-math notation="LaTeX">$\approx 46$ </tex-math></inline-formula> % under cold&#x2013;dry conditions, whereas moderate load variations are negligible within normal ranges. External validation on a <inline-formula> <tex-math notation="LaTeX">$\sim 93~000$ </tex-math></inline-formula> h record shows low root-mean-square and means absolute errors with near-nominal predictive-interval coverage. Collectively, these results establish a diagnostic-to-decision workflow for reliability modeling that improves confidence in lifetime predictions and supports data-informed operation and maintenance.