Reliability Evaluation of Transmission Accuracy for RV Reducers Based on Uncertainty Theory

In reliability evaluation of RV reducers using accelerated degradation tests, practical constraints (e.g., test costs and resource shortages) often lead to insufficient test iterations or small sample volumes. This results in limited insights into the product’s overall degradation trajectory, inadequate data for reliability analysis, and notable epistemic uncertainty. Conventional accelerated degradation models—rooted in probability theory—depend on the large numbers, rendering them ill-suited to address such uncertainty in small-sample scenarios. Uncertainty theory, a modern mathematical framework developed to characterize epistemic uncertainty, has garnered broad academic interest for its strong adaptability to small-sample contexts. Accordingly, this study explores the evaluation of RV reducer reliability using accelerated degradation data and uncertainty theory, aiming to mitigate epistemic uncertainty arising from small sample sizes. Specifically, this work develops a transmission accuracy degradation model for RV reducers based on the Liu process—a core component of uncertainty theory—that incorporates both inter-sample individual variability and the epistemic uncertainty inherent in the degradation process. This study also assesses the reducer’s reliability and service life; comparative analysis against probability-theoretic models confirms the proposed model’s advantages in small-sample scenarios.