A Sensitivity Analysis Workflow for Power Series Compounded Lifetime Models: Evidence From Weibull Power Series Fits

We propose a practical procedure to quantify the time varying influence of parameters on hazard functions for power series compounded lifetime models. The procedure combines likelihood based fitting with a two stage sensitivity analysis and applies to a range of baselines and compounding laws. We demonstrate the approach using the Weibull Power Series (WPS) family on two case studies: Boeing 720 air conditioning failures and Iran inter‐earthquake intervals. In both cases, the baseline shape parameter emerges as the primary driver of hazard at medium and larger times, while the compounding parameter governs early time behaviour before its influence fades. Crucially, when extending the workflow to the more generalized Exponentiated Extended Weibull Power Series (EEWPS) model, we identify a ‘Sensitivity Passivity’ phenomenon, where additional mathematical complexity does not yield significant statistical gain or physical insight. The workflow detects parameter redundancy and the interaction driven competition for interpretability, providing a rigorous, evidence‐based justification for model parsimony. The framework yields practically useful summaries, including the prioritization of parameters for estimation, guidance on early life data collection, and diagnostics for selecting models that balance fitting accuracy with operational simplicity.