Remaining useful life prediction for hard failures using joint model with extended hazard

In this paper, we investigate a joint modeling method for hard failures where both degradation signals and time-to-event data are available. The mixed-effects model is used to model degradation signals, and extended hazard model is used for the time-to-event data. The extended hazard is a general model which includes two well-known hazard rate models, the Cox proportional hazards model and accelerated failure time model, as special cases. A two-stage estimation approach is used to obtain model parameters, based on which remaining useful life for the in-service unit can be predicted. The performance of the method is demonstrated through both simulation studies and a real case study.