A time-discrete and zero-adjusted gamma process model with application to degradation analysis

The standard gamma process is widely used for degradation modelling when the degradation paths are always positive and strictly increasing. Nevertheless, the standard gamma process is considered inappropriate if the observed sample paths are horizontal over several time intervals. Motivated by this phenomenon, we develop a time-discrete and zero-adjusted gamma process model. Statistical inference method of this model is then proposed. To illustrate our proposed model, both simulation study and real data analysis are conducted, whose results demonstrate that the proposed model has satisfactory fit performance and predictive performance.