A two-stage Weibull-gamma degradation model with distinct failure mechanism initiation and propagation stages

Degradation models have become important analytic tools for industrial systems. In this paper, a new two-stage stochastic degradation model is introduced with separate failure mechanism initiation and propagation stages. The new degradation model represents an important advancement in degradation modelling by considering the degradation initiation stage or delay before active degradation propagation is observed. The new model consists of a time-to-event distribution that describes failure initiation or delay in the first stage, concluding when the degradation propagation stage is initiated, which indicates the beginning of the second stage, where degradation is modelled using a stochastic process. The combination of a time-to-event distribution and a stochastic degradation model is realistic and is presented considering three different scenarios: degradation with no residual degradation during Stage 1 or no alarm-threshold, degradation with a deterministic alarm-threshold, and degradation with a random alarm-threshold. A Weibull distribution is adopted for the first degradation initiation stage, and a gamma process is used for the second degradation stage. This model is consistent with many physical failure mechanisms, where there is a time delay before the failure process begins to propagate. This is not surprising because designers often introduce design preventions (e.g., protective coatings) to delay the onset of degradation. In our model, both degradation stages can be accelerated by increasing stresses which are then modelled using a set of covariates and acceleration factors. To demonstrate the model, a bridge steel rebar case study is presented and discussed. Based on extensive experiments and data, reliability analysis and accelerated failure mechanism investigation are performed using the proposed model. The results demonstrate that the new model provides advantages for estimating reliability and physically describing the two stages. It can be concluded that the proposed model is useful for reliability assessment and accelerated degradation test planning.