Equivalent Time Inference for Left-Truncated Degradation Data with Unknown Storage History in Accelerated Degradation Modeling

In accelerated degradation tests of highly reliable products, newly manufactured samples are often scarce, while historical inventories contain naturally aged units with unknown storage histories and left-truncated data. To address this issue, an equivalent time transformation method is proposed to integrate pre-storage degradation with accelerated test data. The degradation of new samples is modeled using a nonlinear Wiener process, with parameters estimated via Bayesian MCMC. The equivalent aging time of stored samples is inferred by maximizing the probability density function, enabling temporal alignment across heterogeneous data sources. The transformed data are then incorporated to reconstruct lifetime distributions. Validation using photomultiplier tube (PMT) data and leave-one-out cross-validation shows reduced RMSE and MAPE. The results demonstrate improved data utilization, enhanced estimation stability, and more accurate reliability prediction under small-sample conditions.