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Uncertainty from heterogeneous degradation paths, limited experimental samples, and exogenous perturbations often complicates accelerated lifetime modeling and prediction. To confront these intertwined challenges, a Wiener process-based robust framework is developed. The proposed approach incorporates random-effect structures to capture unit-to-unit variability, adopts interval-based inference to reflect sampling limitations, and employs a hybrid estimator, combining Huber-type loss with a Metropolis–Hastings algorithm, to suppress the influence of external disturbances. In addition, a quantitative stress–parameter linkage is established under the accelerated factor principle, supporting consistent transfer from accelerated testing to normal conditions. Validation on contact stress relaxation data of connectors confirms that this methodology achieves more stable parameter inference and improves the reliability of lifetime predictions.