Bayesian inference for a novel hierarchical accelerated degradation model considering the mechanism variation

For highly reliable products, accelerated thermal degradation tests are efficient to provide feedback on reliability information. In accelerated thermal degradation tests, the degradation data collected at the elevated temperatures are used to extrapolate the performance of products at the normal temperature. An important tool in such extrapolation is the Arrhenius model, in which the activation energy is generally assumed to be constant. However, in some practical accelerated thermal degradation tests of polymeric materials, a variation of the underlying degradation mechanism is induced when the temperature rises to a certain high level, resulting in a change in the activation energy. Motivated by this phenomenon, we propose a two-stage Arrhenius model. The two stages correspond to the lower and higher temperature ranges with different activation energies. Then, this new model is incorporated to the degradation model, yielding a novel hierarchical model for the accelerated thermal degradation test data from polymeric materials involving a mechanism variation. Furthermore, the Bayesian method is adopted for parameter inference, and the lifetime distribution is obtained subsequently. A practical example of polysiloxane rubbers demonstrates the effectiveness of the proposed model.