Time-Invariant Learning and History-Based Inference for Time-Varying Survival Models in Predictive Maintenance

Technical failure prediction is commonly carried out using time-invariant models, which analyze a single object state, and time-varying models, which consider state sequences over time. In practice, monitoring data is collected as temporal chains reflecting system degradation. Considering system failure as a terminal event, survival analysis methods provide an estimation of the event risk at future times. However, most existing approaches exploit the time-varying data only during model training, while at the inference stage, they rely on the last observation. The gap between training and inference can lead to the loss of operational history, limiting model effectiveness in reliability analysis, where failure risk depends on accumulated degradation rather than the current state. This work proposes a methodology to address this gap. The proposed algorithm for sampling time-invariant observations from complete temporal monitoring chains enables training time-invariant models on time-varying data. A class of time-conditioned models uses a prediction horizon as a covariate, allowing flexible construction of individual forecasts on a continuous time scale. To utilize operational history during the inference, we propose a method for aggregating sequential model predictions collected at various time points. The weighting schemes control the contribution of past observations and define a trade-off between survival function accuracy and risk-based ranking quality. An experimental study on the Backblaze hard drive failure dataset compares the classical time-varying Cox model, alternative statistical formulations, and the proposed time-conditioned neural network. The results demonstrate that the proposed algorithm for sampling time-invariant observations improves the performance of time-invariant models, while prediction aggregation significantly enhances survival function approximation measured by the Integrated Brier Score compared to single-point prediction. The proposed time-conditioned neural network shows the best overall performance. The results confirm that the proposed methodology enhances historical data utilization and improves failure prediction accuracy in intelligent industrial monitoring systems.